Geometry Theorems and Problems - Recent Additions (Page
8 of 15)
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![Euclidean Geometry](euclidean_geometry_17.jpg) |
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![Parallel lines](../problem/p549_parallel_angle_1.jpg) |
Problem
549.
Parallel lines, Transversal, Angle Sums. |
![Triangle, Circumcircles, Circumcenters, Concyclic](../problem/p548_triangle_circumcenters.jpg) |
Problem
548.
Triangle, Transversal, Four Circumcircles, Circumcenters, Concyclic Points,
Similarity. |
![Triangle, Four circumcircles](../problem/p547_triangle_circumcircles.jpg) |
Problem
547.
Triangle, Transversal, Four Circumcircles, Concurrency. |
![Circumcircle Index](../center/circumcircle_index_1.jpg) |
Circumcircle
Index.
|
![Triangle, Angle Trisectors, Equilateral](../problem/p546_triangle_trisector_1.jpg) |
Problem
546.
Triangle, Angle Trisectors, 60 Degrees, Equilateral triangle. |
![Acute Triangle with altitudes and squares](../problem/p545_acute_triangle_1.jpg) |
Problem
545.
Acute Triangle, Squares, Altitudes, Area, Measure. |
![Right Triangle, Altitude, Median, Equal angles, Measure](../problem/p544_right_triangle_1.jpg) |
Problem
544.
Right Triangle, Altitude, Median, Equal angles, Measure. |
![Geometry problems 341-350](../math_geometry_online_courses/geometry_problems_341_350_1.jpg) |
Geometry Problems
341 -
350.
Triangle, Quadrilateral, Pentagon, Hexagon, Inscribed circle, Tangent, Semiperimeter, Equal circles, Concurrent lines, Altitude, Concyclic Points, Cevian, Incircle. |
![Right Triangle, Altitude, Angle Bisector, Median](../problem/p543_right_triangle_1.jpg) |
Problem
543.
Right Triangle, Altitude, Angle Bisector, Median. |
![Right triangle, Altitude, Angle Bisectors, 90 Degrees](../problem/p542_right_triangle_1.jpg) |
Problem
542.
Right Triangle, Altitude, Angle Bisector, Perpendicular, 90 Degrees. |
![Right triangle, Altitude, Angle Bisector](../problem/p541_right_triangle_1.jpg) |
Problem
541.
Right Triangle, Altitude, Angle Bisector, Congruence. |
![Geometry problems 331-340](../math_geometry_online_courses/geometry_problems_331_340_1.jpg) |
Geometry Problems
331 -
340.
Square, Circle, Similarity, Cyclic quadrilateral, Trapezoid, Triangle, Isosceles, Circumcircle, Incircle, Diagonal, Tangent, Perpendicular, Parallel, Concyclic points. |
![Geometry problems 321-330](../math_geometry_online_courses/geometry_problems_321_330_1.jpg) |
Geometry Problems
321 -
330.
Triangle, Square, Circle, Area, Cyclic quadrilateral, Tangent, Incenter, Circumcenter, Excircle, Midpoint, Altitude, Collinearity, Concurrence, Isosceles, Equilateral, Parallel, Perpendicular, Diameter, Concyclic. |
![Geometry problems 311-320](../math_geometry_online_courses/geometry_problems_311_320_1.jpg) |
Geometry Problems
311 -
320.
Circle, Semicircle, Chord, Diameter, Tangent, Cyclic quadrilateral, Geometric mean, Square, Right triangle, Altitude, Collinearity, Circumcircle, Incenter, Excenter. |
![Geometry problems 301-310](../math_geometry_online_courses/geometry_problems_301_310_1.jpg) |
Geometry Problems
301 -
310.
Circle, Tangent, Secant, Square, Triangle, Angle Bisector, 45, 60, 90, 120 Degrees, Side, Nonagon, Midpoint, Arc, Diagonal, Semicircle. |
![Geometry problems 231-240](../math_geometry_online_courses/geometry_problems_231_240_1.jpg) |
Geometry Problems 231 - 240.
Triangle, Quadrilateral, Square, Parallelogram, Trapezoid, Altitude, Distances, Midpoint, Perpendicular, Transversal. |
![Right triangle, Square, Area](../pythagoras/p540_right_triangle_area_1.jpg) |
Problem
540.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
![Geometry problems 291-300](../math_geometry_online_courses/geometry_problems_291_300_1.jpg) |
Geometry Problems 291 -
300.
Triangle, Circle, Square, Congruence, Similarity, Circumradius, Perpendicular, Parallel, Secant, Tangent, Chord, Intersection, Midpoint, Radius, Angle. |
![Right triangle, Square, Area](../pythagoras/p539_right_triangle_area_1.jpg) |
Problem
539.
Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras. |
![Geometry problems 281-290](../math_geometry_online_courses/geometry_problems_281_290_1.jpg) |
Geometry Problems 281 -
290.
Triangle, Square, Circle, Octagon, Congruence, Isosceles, Equilateral, 90 Degrees, Circular Sector, Semicircle, Tangent, Radius, Diameter, Harmonic Mean. |
![Triangle, Circumcircle, Perpendicular Bisector](../problem/p538_triangle_circle_1.jpg) |
Problem
538.
Triangle, Perpendicular Bisector, Circumcircle, Midpoint. |
![Rectangle, Midpoint, Diagonal, Angle Bisector](../problem/p537_rectangle_bisector_1.jpg) |
Problem
537.
Rectangle, Midpoints, Diagonal, Angle Bisector. |
|
Problem
536.
Intersecting Circles, Chord, Perpendicular. |
![Sawayama - Thebault Theorem](../problem/p535_sawayama_thebault_1.jpg) |
Problem
535.
Sawayama - Thebault's theorem: Triangle, Incircle, Circle, Center, Tangent,
Collinear. |
![Right triangle, square, area](../problem/p534_right_triangle_area_1.jpg) |
Problem
534.
Right Triangle, Squares, Perpendicular, Dissection, Areas. |
![Geometry problems 271-280](../math_geometry_online_courses/geometry_problems_271_280_1.jpg) |
Geometry Problems 271 -
280.
Circle, Quadrilateral, Square, Tangent, Cube, Triangle, Isosceles, Area, 90-80-80-20 Degrees, Circumcircle, Sagitta, Inradius, Chord, Perpendicular. |
![Geometry problems 261-270](../math_geometry_online_courses/geometry_problems_261_270_1.jpg) |
Geometry Problems 261 -
270.
Regular Polygon, Pentagon, Hexagon, Circle, Tangent, Similarity, Triangle, Hypotenuse, Catheti, Geometric Mean, Altitude, Projection, Fractional Exponent. |
![Problem 533: Euclid's Elements Book XIII, Proposition 10](euclid_elements_book_xiii_10_17.jpg) |
Problem
533.
Euclid's
Elements, Book XIII, Proposition 10. One page visual illustration. |
![Geometry problems 251-260](../math_geometry_online_courses/geometry_problems_251_260_1.jpg) |
Geometry Problems 251 -
260.
Parallelogram, Rectangle, Triangle, Square, Circle, Area, Side, Equilateral, Isosceles, Centroid, Distance, Vertex, Circumcircle, Incircle, Tangent, Diagonal. |
![Brahmagupta Theorem and Problems Index](../math_geometry_online_courses/brahmagupta_index.jpg) |
Brahmagupta Theorem and Problems - Index
Brahmagupta (598–668) was an Indian mathematician and astronomer who discovered a neat formula for the area of a cyclic quadrilateral. |
![Morphing Platonic Solds](solid_geometry_morphing_v.jpg) |
Solid Geometry: Morphing Platonic Solids. Sacred geometry, Video and News.
|
![Triangle, Area](../problem/p532_triangle_area_1.jpg) |
Problem 532.
Triangle, Circumcircle, Equal Angles, Perpendicular, Area. |
![Ptolemy Theorem and Problems Index](../math_geometry_online_courses/ptolemy_theorem_index_1.jpg) |
Ptolemy's Theorems and Problems - Index. |
![Semiperimeter, Perimeter Index](semiperimeter_index_1.jpg) |
Semiperimeter, Perimeter Index.
Theorems and Problems. |
![Triangle, Semiperimeter](../problem/p531_triangle_semiperimeter.jpg) |
Problem 531.
Triangle, Angle Bisector, Midpoint, Parallel, Perimeter, Semiperimeter. |
![Geometry problems 241-250](../math_geometry_online_courses/geometry_problems_241_250_1.jpg) |
Geometry Problems 241 - 250.
Triangle, Quadrilateral, Congruence, Area, Parallelogram, Square, Diagonal, Center, Napoleon, Median, Midpoint. |
![Cyclic quadrilateral, Diagonal, Diameter](../problem/p530_cyclic_quadrilateral_1.jpg) |
Problem 530.
Cyclic Quadrilateral, Diagonal, Diameter, Perpendicular, Congruence. |
![Right Trapezoid, Circle, Diameter](../problem/p529_trapezoid_circle_1.jpg) |
Problem 529.
Right Trapezoid, Circle, Diameter. |
![Triangle, Medians, Perpendicular](../problem/p528_triangle_medians_1.jpg) |
Problem 528.
Triangle, Medians, Perpendicular, Measurement. |
![Circle, Tangent, Secant, Midpoint](../problem/p527_circle_tangent_secant_.jpg) |
Problem 527.
Circle, Tangent, Secant, Chord, Midpoint, Measurement. |
![Equilateral triangle, Circumcircle](../problem/p526_equilateral_triangle_1.jpg) |
Problem 526.
Equilateral Triangle, Circumcircle, Chord, Measurement. |
![Geometry problems 221-230](../math_geometry_online_courses/geometry_problems_221_230_1.jpg) |
Geometry Problems 221 - 230.
Isosceles, Equilateral triangle, Viviani's theorem, Altitude, Distances, Regular Polygon, Apothem, Centroid, Midpoint, Perpendicular, Transversal.. |
![Circle, Tangent, Diameter, Radius, Congruence](../problem/p525_circle_tangent.jpg) |
Problem 525.
Circles, Diameter, Tangent, Radius, Congruence, Measurement. |
![Circle with equilateral triangles](../problem/p524_circle_equilateral_tri.jpg) |
Problem 524.
Circle, Equilateral Triangles, Midpoint, Side, Measurement. |
![Tangent Circles](../problem/p523_tangent_circle_1.jpg) |
Problem 523.
Tangent Circles, Diameter Perpendicular, Collinearity. |
![Geometry Problem: Right triangle, Circle, Tangent](../problem/p522_triangle_circle_1.jpg) |
Problem 522.
Right Triangle, Circle, Diameter, Tangent. |
![Triangle, Three Squares, Altitude, Area](../problem/p521_triangle_squares_area.jpg) |
Problem
521.
Triangle with three Squares, Altitude, Rectangle, Area. |
![Geometry problems 211-220](../math_geometry_online_courses/geometry_problems_211_220_1.jpg) |
Geometry Problems
211 -
220.
Equilateral triangle, Quadrilateral, Area, Cyclic Quadrilateral, 60 Degree, Angle Bisector, 120, incircle, Inradius, Semicircle, Tangent, Concurrency, Right triangle, Altitude, Projection, Rhombus, Perpendicular, Arithmetic Mean, Distance. |
![Triangle with six Squares](../problem/p520_six_squares_triangle.jpg) |
Problem
520.
Triangle with six Squares, Ratio, Area. |
![Triangle with Squares and Rectangles](../problem/p519_triangle_square_area_1.jpg) |
Problem
519.
Triangle, Squares, Altitude, Perpendicular, Rectangle, Area. |
![Geometry problems 191-200](../math_geometry_online_courses/geometry_problems_191_200_1.jpg) |
Geometry Problems 191 -
200.
Triangle, Circle, Square, Area, Circle, Diameter, Altitude, Orthocenter, Semiperimeter, Inradius, Exradius, Quadrilateral, Angle, Tangent, Right triangle. |
![Geometry problem 518](../problem/p518_parallelogram_square_1.jpg) |
Problem
518.
Parallelogram, Five Squares, Centers, 45 Degrees, Measure. |
![Right triangle with six squares](../problem/p517_squares_triangle_1.jpg) |
Problem
517.
Right Triangle, Six Squares, Areas. |
![Triangle, Cevian, Congruence, Angles](../problem/p516_triangle_angle_cevian.jpg) |
Problem
516.
Triangle, Cevian, Congruence, Angles. |
![Triaangle, Double-angle, Altitude](../problem/p515_triangle_double_angle.jpg) |
Problem
515.
Triangle, Double Angle, Altitude, Measure. |
![Geometry problems 181-190](../math_geometry_online_courses/geometry_problems_181_190_1.jpg) |
Geometry Problems 181 -
190.
Right Triangle, Trapezoid, Square, Intersecting Circles, Circular Sector, 90 Degrees, Angles, Trisection, Hypotenuse, Distance, Incenter, Altitude, Diagonal, 45 Degrees, Tangent, Chord, Perpendicular. |
![Triangle with five squares](../problem/p514_squares_triangle_1.jpg) |
Problem
514.
Triangle, Five Squares, Line, Area. |
![Geometry problem Triangle with double angle](../problem/p513_triangle_double_angle.jpg) |
Problem
513.
Triangle, Double Angle, Exterior Angle Bisector, Measure. |
![Geometry problems 171-180](../math_geometry_online_courses/geometry_problems_171_180_1.jpg) |
Geometry Problems 171 -
180.
Area, Triangle, Quadrilateral, Circle, Parallelogram, Trapezoid, Square, Rhombus, Diagonal, Angle, Tangent, Trisection. |
![Geometry problems 161-170](../math_geometry_online_courses/geometry_problems_161_170_1.jpg) |
Geometry Problems 161 -
170.
Area, Triangle, Parallelogram, Trapezoid, Pentagon, Diagonal, Midpoint, Octagon. |
![Triangle with squares problem](../problem/p512_triangle_square_1.jpg) |
Problem
512.
Triangle with three squares and concurrency. |
![Online education: Geometry Problem 511](../problem/p511_triangle_double_angle.jpg) |
Problem
511.
Triangle, Double Angle, Angle Bisector, Measure. |
![Triangle with three squares](../problem/p510_triangle_square_1.jpg) |
Problem
510.
Triangle, Three Squares, Midpoints, Concurrency. |
![Triangle, 120 Degrees, Angles, Congruence, Mind Map](../problem/p509_triangle_120_degrees_1.jpg) |
Problem
509.
Triangle, 120 Degrees, Angles, Congruence, Mind Map. |
![Geometry problems 151-160](../math_geometry_online_courses/geometry_problems_151_160.jpg) |
Geometry Problems 151 -
160.
Triangle, Quadrilateral, Area, Trisection, Circle, Proportion, Diagonal, Chord,Inradius, Circumradius, Exradius, Euler, distance, Incenter, Circumcenter, Excenter, Incircle, Circumcircle. |
![Triangle with three squares](../problem/p508_triangle_square_area_1.jpg) |
Problem
508.
Triangle with three Squares, Four triangle of equal Area. |
![Triangle, 120 Degrees, Congruence, Angle](../problem/p507_triangle_120_degrees_1.jpg) |
Problem
507.
Triangle, Interior Point, 120 Degrees, Congruence, Angle. |
![Triangle with Three Squares, Center, Midpoint](../problem/p506_triangle_square_center.jpg) |
Problem
506.
Triangle with Three Squares, Center, Midpoint, Perpendicular. |
![Right triangle, Cevian, Angles](../problem/p505_right_triangle_angle_1.jpg) |
Problem
505.
Right Triangle, Cevian, Sum of Segments, Angles. |
![Equilateral Triangle, Angles, 45, 60 Degrees](../problem/p504_equilateral_triangle.jpg) |
Problem
504.
Equilateral Triangle, Angles, 45, 60 Degrees. |
![Ten Geometry Problems, Visual Index](../math_geometry_online_courses/ten_geometry_problems_i.jpg) |
Ten Geometry Problems, Visual Index |
![Triangle with Three Squares](../problem/p503_triangle_square_center.jpg) |
Problem
503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency. |
![Geometry Problems 141-150](../math_geometry_online_courses/geometry_problems_141_150.jpg) |
Geometry Problems 141 -
150.
Triangle, Quadrilateral, Parallelogram, Incircle, Incenter, Tangent, Parallel, Perimeter, Area, Inradius, Circumradius, Midpoint, Varignon, Trisection. |
![Triangle, Two Squares, Midpoint, Perpendicular, Half the measure](../problem/p502_triangle_square_median.jpg) |
Problem
502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure. |
![Triangle, Two Squares, Center, Midpoint](../problem/p501_triangle_square_center.jpg) |
Problem
501.
Triangle, Two Squares, Center, Midpoint, another Square. |
![Circle, Diameter, Chord, Perpendicular](../problem/p500_circle_diameter_1.jpg) |
Problem
500.
Circle, Diameter, Chord, Perpendicular, Measure. |
![Triangle, Two Squares, Perpendicular](../problem/p499_triangle_squares_1.jpg) |
Problem 499.
Triangle, Two Squares, Perpendicular. |
![Triangle, Angle Bisector, Double Angle](../problem/p498_triangle_bisector_1.jpg) |
Problem 498.
Triangle, Angle Bisector, Double Angle, Measure. |
![Triangle, Two Squares, Centers, Midpoint, 90 Degrees](../problem/p497_triangle_squares_1.jpg) |
Problem 497.
Triangle, Two Squares, Centers, Midpoint, 90 Degrees. |
![Triangle with Squares, 90 degrees](../problem/p496_triangle_squares_1.jpg) |
Problem 496.
Triangle, Two Squares, 90 Degrees, Concurrency, Angle Bisectors. |
![Triangle with 120 degrees](../problem/p495_triangle_120_degrees_1.jpg) |
Problem 495.
Triangle, 120 Degrees, Angle Bisectors. |
![Geometry Problems 121-130](../math_geometry_online_courses/geometry_problems_121_130.jpg) |
Geometry Problems
121 -
130.
Triangle, Area, Similarity, Trisection, Hexagon, Star, Incenter, Centroid, Parallel, Proportions, Angle Bisector, Ratio |
![Elearn 494: Circular Sector, 90 Degrees](../problem/p494_circular_sector_1.jpg) |
Problem 494.
Circular Sector, 90 Degrees, Semicircle, Chord, Parallel. |
![Geometry Problems 111-120](../math_geometry_online_courses/geometry_problems_111_120.jpg) |
Geometry Problems
111 -
120.
Orthogonal Circles, Triangle, Square, Area, Incircle, Excircle, Tangent, Incenter |
![The Simson Line Index](simson_line_i.jpg) |
The Simson Line,
Theorems and Problems - Index. |
![Geometry Problems 101-110](../math_geometry_online_courses/geometry_problems_101_110.jpg) |
Geometry Problems
101 -
110.
Angle, Equilateral Triangle, Pythagorean Theorem, Median, Heron, Cevian, Contact Triangle. |
![Elearn 493: Right triangle, Circumcircle, Perpendicular](../problem/p493_triangle_circle_1.jpg) |
Problem 493.
Right Triangle, Circumcircle, Perpendicular, Chord. |
![Elearn 492: Quadrilateral, CIrcle, Perpendicular, Parallel](../problem/p492_quadrilateral_circle_1.jpg) |
Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel. |
![Geometry Problems 91-100](../math_geometry_online_courses/geometry_problems_91_100.jpg) |
Geometry Problems
91 -
100.
Similarity, Triangles, Altitude, Parallel, Circumcircle, Parallelogram, Incenter, Area, Centroid, Quadrilateral, Archimedes, Pythagoras. |
![Elearn 491: Square, Incircles, Radius, Side](../problem/p491_square_circle_1.jpg) |
Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius. |
![Geometry Problem 81-90](../math_geometry_online_courses/geometry_problems_81_90.jpg) |
Geometry Problems
81 -
90.
Triangle, Quadrilateral, Circle, Incircle, Circumcircle, Excircle, Inradius, Circumradius, Exradius, Contact Triangle, Area, Midpoint. |
![Elearn 490: Circular Sector Area](../problem/p490_circular_sector_area_1.jpg) |
Problem 490.
Tangent Circles, Arc, Radius, Circular Sector, Area. |
![Elearn 489: Parallelogram, Areas](../problem/p489_parallelogram_area_1.jpg) |
Problem 489.
Parallelogram, Triangle, Quadrilateral, Area. |
![Triangle, Cevian, Circle, Concurrency](../problem/p488_triangle_circle_1.jpg) |
Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle. |
![Geometry Problems 71-80](../math_geometry_online_courses/geometry_problems_71_80.jpg) |
Geometry Problems
71 -
80.
Cyclic Quadrilateral, Intersecting Circles, Area, Inradius, Incircle. |
![Circle, Area, 90 Degrees](../problem/p487_circle_area_1.jpg) |
Problem 487.
Intersecting
Circles, Area, Diameter, Parallel, 90 Degrees. |
![Tangent circles, Midpoint, Arc, Collinear](../problem/p486_tangent_circles_1.jpg) |
Problem 486.
Tangent circles, Chord, Arc, Midpoint, Collinearity, Congruence. |
![Square, Circles, Tangent](../problem/p485_square_circles_1.jpg) |
Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement. |
![Square, Angle, 90 degrees, Proportion](../problem/p484_square_triangle_1.jpg) |
Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion. |
![Geometry problems visual index](../math_geometry_online_courses/geometry_problem_index_1.jpg) |
Geometry Problems - Visual Index. |
![Triangle, Square, 90 degrees](../problem/p483_square_triangle_1.jpg) |
Problem 483.
Square, Angle, 90 degrees, Measurement. |
![Triangle, Circumcircle, Incircle, Excircle](../problem/p482_triangle_circle_1.jpg) |
Problem 482.
Triangle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic Points. |
![Triangle, Altitude, Perpendicular, Angle](../problem/p481_triangle_angle_1.jpg) |
Problem 481.
Triangle, Altitude, Cevian, Perpendicular, Angle. |
![Geometry Problems 61-70](../math_geometry_online_courses/geometry_problems_61_70.jpg) |
Geometry Problems
61 -
70.
Triangle, Quadrilateral, Circle, Cyclic, Similarity. |
![Triangle, circle, angle, altitude](../problem/p480_circle_angle_1.jpg) |
Problem 480.
Triangle, Circle, Center, Altitude, Angle, Circumcenter. |
![Triangle COncurrency, Transversal, Proportion](../problem/p479_triangle_concurrency_1.jpg) |
Problem 479.
Triangle, Cevians, Concurrency, Transversal, Proportion. |
![Triangle, Sides, Circumradius](../problem/p478_triangle_circle_1.jpg) |
Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle. |
![Parallelogram, triangle, quadrilateral, area](../problem/p477_parallelogram_area_1.jpg) |
Problem 477.
Parallelogram, Triangle, Quadrilateral, Area. |
![Geometry problems 51-60](../math_geometry_online_courses/geometry_problems_51_60.jpg) |
Geometry Problems
51 -
60.
Triangle, Quadrilateral, Circle, Cyclic Quadrilateral. |
![Triangle, Circumcenter, Angle](../problem/p476_triangle_circumcircle_.jpg) |
Problem 476.
Triangle, Circumcenter, Circumcircle, Angles. |
![Tangent circles, secant, parallel](../problem/p475_circle_tangent_1.jpg) |
Problem 475.
Tangent Circles, Secant, Tangent, Parallel. |
![Geometry Problems 41-50](../math_geometry_online_courses/geometry_problems_41_50.jpg) |
Geometry Problems
41 -
50.
Triangle, Sangaku, Quadrilateral, Circle, 30-60 Degrees. |
![Parallelogram, Diagonal, Circle](../problem/p474_parallelogram_circle_1.jpg) |
Problem 474.
Parallelogram, Diagonal, Circle, Vertex. |
![Triangle, Area, Similarity](../problem/p473_similarity_area_1.jpg) |
Problem 473.
Triangle, Parallel, Side, Parallelogram, Area, Similarity. |
![Triangle, Area, Similarity](../problem/p472_similarity_area_1.jpg) |
Problem 472.
Triangle, Parallel, Side, Parallelogram, Area, Similarity. |
![Online education degree: geometry problems 21-30](../math_geometry_online_courses/geometry_problems_21_30.jpg) |
Geometry Problems 21 -
30.
Right triangle, Altitude, Incircle and inradius, Congruence, Circle. |
![Triangle area, parallel, concurrency](../problem/p471_similarity_area_1.jpg) |
Problem 471.
Triangle, Parallel, Side, Concurrency, Area, Similarity. |
![Online education degree: geometry problems 11-20](../math_geometry_online_courses/geometry_problems_11_20.jpg) |
Geometry Problems 11 -
20.
Angle, Angle bisector, Triangle, Altitude, Median, Congruence, Cevian, Circle,
Excircle, Excenter, Inradius, Exradius |
![Triangle area, Similarity](../problem/p470_similarity_area_1.jpg) |
Problem 470.
Triangle, Parallel, Side, Parallelogram, Area, Similarity. |
![Online education degree: geometry problems 1-10](../math_geometry_online_courses/geometry_problems_1_10.jpg) |
Geometry Problems 1 - 10.
Angle, Triangle, Quadrilateral, Congruence, 20, 30, 45, 60, 80, 120 degrees,
Median, Auxiliary lines. |
![Isosceles triangle, midpoint, transversal](../problem/p469_isosceles_triangle_1.jpg) |
Proposed
Problem 469.
Isosceles triangle, Midpoint, Transversal, Congruence. |
![Circle, chord, congruence, angle](../problem/p468_circle_chord_angle_1.jpg) |
Proposed
Problem 468.
Circle, Chord, Midpoint, Congruence, Angle. |
![Concentric circles](../problem/p467_concentric_circles_1.jpg) |
Proposed
Problem 467.
Concentric Circles, Chord, Tangent, Congruence, Measurement. |
![Concentric circles, secant, congruence](../problem/p466_concentric_circles_1.jpg) |
Proposed
Problem 466.
Concentric Circles, Secant, Congruence, Measurement. |
![Square, Arc, 90 degrees](../problem/p465_square_90_degree_1.jpg) |
Proposed
Problem 465.
Square, Arc, Angle, 90 Degrees, Measurement. |
![Napoleon Theorem and Problem Index](napoleon_theorem_index_17.jpg) |
Napoleon's theorems and problems, Index. |
![Square, Arc, Angle](../problem/p464_square_arc_120_degree_.jpg) |
Proposed
Problem 464.
Square, Arcs, Center, Angle, 90 Degrees, 120 Degrees. |
![Concentric circles, Index](../circle/concentric_circles_index.jpg) |
Concentric
Circles.
Index.
Theorems and Problems.
|
![Concentric Circles Definition](../circle/concentric_circles_def_1.jpg) |
Concentric
Circles Definition. |
![Concentric Circles, Tangent, Area](../problem/p463_circle_triangle_area_1.jpg) |
Proposed
Problem 463.
Three Concentric Circles, Secant, Tangent, Triangle, Area. |
![Square, Circle, Arc, 90 Degrees](../education/p462_circle_square_radius.jpg) |
Proposed
Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement. |
![Three tangent circles, Radius, Distance](../education/p461_circle_tangent_radius.jpg) |
Proposed
Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement. |
![Circle, Tangent, Perpendicular, Radius](../education/p460_circle_tangent_radius.jpg) |
Proposed
Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement. |
![Right triangle, Squares](../education/p459_right_triangle_square_.jpg) |
Proposed
Problem 459.
Right triangle, Squares, Distance, Measurement. |
![Square, Circle, Tangent](../education/p458_triangle_circle_sector.jpg) |
Proposed
Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement. |
![Triangle Brocard point](../education/p457_triangle_brocard_1.jpg) |
Proposed
Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius. |
![Three tangent circles](../education/p456_tangent_circles_1.jpg) |
Proposed
Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear. |
![Rhombus, Circle](../education/p455_rhombus_circle_1.jpg) |
Proposed
Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees. |
![Triangle, Incircle, Inradius](../education/p454_triangle_incircle_1.jpg) |
Proposed
Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius. |
![Circular segments](../education/p453_circular_segment_1.jpg) |
Proposed
Problem 453.
Intersecting Circles, Tangent, Circular Segment, Congruence, Area. |
![Triangle centers, visual index](../center/triangle_center_visual_inde.jpg) |
Triangle Centers,
Visual Index. |
![Fermat Point](../center/fermat_point_1.jpg) |
Fermat Point.
|
![Vecten Point](../center/vecten_point_1.jpg) |
Vecten
Outer Point.
|
![Triangle, Circle, Tangent](../education/p452_triangle_circle_1.jpg) |
Proposed
Problem 452.
Triangle, Circle, Tangent, Proportional Segments. |
![Triangle, median](../education/p451_triangle_median_1.jpg) |
Proposed
Problem 451.
Triangle, Median, Congruence, Proportional Segments. |
![Triangle, Median, Cevian](../problem/p450_triangle_median_1.jpg) |
Proposed
Problem 450.
Triangle, Median, Cevian, Congruence, Proportional Segments. |
![Circle, Diameter, Sagitta](../problem/p449_circle_sagitta_1.jpg) |
Proposed
Problem 449.
Congruent Tangent Circles, Diameter, Sagitta, Arc, Perpendicular, Chord. |
![Tangent circles, diameter](../problem/p448_tangent_circle_1.jpg) |
Proposed
Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord. |
![Complete Quadrilateral](../problem/p447_complete_quadrilateral.jpg) |
Proposed
Problem 447.
Complete Quadrilateral, Inradii, Exradii, Sides. |
![Complete quadrilateral](complete_quadrilateral_inde.jpg) |
Complete Quadrilateral Index.
|
![Quadrilateral Area](../problem/p446_quadrilateral_area_1.jpg) |
Proposed
Problem 446.
Quadrilateral Area, Dividing the sides into 5 equal parts. |
![Three Tangent Circles](../problem/p445_tangent_circles_1.jpg) |
Proposed
Problem 445.
Three Tangent Circles, Tangency Points, Circumradius. |
![Tangent Circles](../problem/p444_tangent_circles_1.jpg) |
Proposed
Problem 444.
Internally Tangent circles, Secant line, Chords, Angles, Congruence. |
![Intersecting circles](../problem/p443_intersecting_circles_1.jpg) |
Proposed
Problem 443.
Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles. |
![Triangle, Median, Transversal](../problem/p442_triangle_median_1.jpg) |
Proposed
Problem 442.
Triangle, Median, Cevian, Transversal, Congruent Angles. |
![Problem 441: Quadrilateral, Area](../problem/p441_quadrilateral_area_1.jpg) |
Proposed
Problem 441.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity. |
![Geometry problem 440](../problem/p440_incenter_angle_1.jpg) |
Proposed
Problem 440.
Triangle, Incircle, Incenter, Angle Bisector, Tangency Points, Circle, Angles. |
![Marion Walter's theorem and related topics](marion_walter_theorem_index.jpg) |
Marion Walter's Theorem
and Related Topics: Index |
![Circle, Angle, Incenter, Isosceles triangle](../problem/p439_circle_angle_1.jpg) |
Proposed
Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle. |
![Tangent Circles, Chords, Perpendiculars](../problem/p438_circle_chord_1.jpg) |
Proposed
Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement,
Parallel lines. |
![Tangent Circles, Chords, Perpendiculars](../problem/p437_circle_chord_1.jpg) |
Proposed
Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement. |
![Tangent Circles, Chords, Perpendiculars](../problem/p436_circle_chord_1.jpg) |
Proposed
Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement. |
![Distance between the incenter to the centroid](../center/distance_incenter_centroid_.jpg) |
Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c. |
![Distance between triangle centers](../center/distance_triangle_centers.jpg) |
Distances between Triangle Centers
Index.
|
![Triangle, CIrcle, Incircle, Inradius](../problem/p435_circle_radius_1.jpg) |
Proposed
Problem 435.
Triangle, Incircle, Inradius, Congruent circles, tangent, Measurement. |
![Quadrilateral, transversal, ratio, similarity](../problem/p434_quadrilateral_ratio_1.jpg) |
Proposed
Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity. |
![Problem 433: Quadrilateral, Area](../problem/p433_quadrilateral_area_1.jpg) |
Proposed
Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity. |
![Problem 432: Trapezoid, Parallel, Similarity](../problem/p432_trapezoid_parallel_1.jpg) |
Proposed
Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal. |
![Quadrilateral, Midpoint diagonals](../problem/p431_quadrilateral_similar_.jpg) |
Proposed
Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal. |
![Transversal Line, Index](transversal_line_index_1.jpg) |
Transversal Lines. |
![Inscribed and Circumscribed regular Pentagon, Areas](../problem/p430_regular_pentagon_17.jpg) |
Proposed
Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas. |
![Obtuse Angle Index](obtuse_angle_index_17.jpg) |
Obtuse Angle.
Theorems and Problems. |
![Isosceles triangle 80-20-80](isosceles_80_20_80_index.jpg) |
Isosceles Triangle
80-20-80. Index |
![Regular pentagon](../problem/p429_regular_pentagon_17.jpg) |
Proposed
Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement. |
![Quadrant of a circle, Square](../problem/p428_circle_square_17.jpg) |
Proposed
Problem 428.
Quadrant of a circle, Square, Angle bisector, Measurement. |
![Euclid's Elements Book i,1 Proposition 8 SSS](euclid_book_i_8_sss_1.jpg) |
Euclid's Elements Book I, Proposition
8: (Side-Side-Side SSS Congruence) |
![Euclid's Elements Book I,1 Proposition 7](euclid_book_i_7_congruence.jpg) |
Euclid's Elements Book I, Proposition
7
Given two straight lines constructed on a straight line (from its extremities) and meeting in a point,... |
![Triangle, Altitudes](../problem/p427_triangle_altitude_17.jpg) |
Proposed
Problem 427.
Triangle, Two Altitudes, Square of a Side. |
![Circumradius, Circumcenter, Triangle](../problem/p426_circumradius_cevian_17.jpg) |
Proposed
Problem 426.
Triangle, Circumradius, Circumcenter, concurrent Cevians. |
![Euclid's Elements Book I,1 Proposition 5, Isosceles Triangle](euclid_book_i_5_isosceles_1.jpg) |
Euclid's Elements Book I, Proposition 5: (Pons Asinorum) Isosceles triangles |
![Area of a square](area_square_index_17.jpg) |
Area
of a Square Index.
|
![Euclid's Elements Book I Proposition 6](euclid_book_i_6_triangle_1.jpg) |
Euclid's Elements Book I, Proposition
6: Converse of I.5 |
![Geometry classes problem 425](../problem/p425_quadrilateral_angle_17.jpg) |
Proposed
Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence. |
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