Geometry Theorems and Problems - Recent Additions (Page
10 of 15)
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![Euclidean Geometry](euclidean_geometry_17.jpg) |
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![Triangle, Angles](../problem/p281_triangle_angle_17.jpg) |
Proposed Problem
281.
Triangles, Angles, Isosceles, Equilateral. |
![Cyclic Quadrilateral Index](cyclic_quadrilateral_index_.jpg) |
Cyclic Quadrilateral.
Index |
![Angle Bisector Index](angle_bisector_index_17.jpg) |
Angle Bisector.
Index. |
![Angle Index](angle_index_17.jpg) |
Angles. |
![Quadrilateral, Perpendicular, Squares, Area](../problem/p280_quadrilateral_squares_.jpg) |
Proposed Problem
280.
Quadrilateral, Perpendiculars, Area of Squares. |
![Polygon Classification](polygon_classification_17.jpg) |
Polygon Classification. Interactive Mind Map. |
![Sacred Geometry Index](sacred_geometry_index_17.jpg) |
Sacred
Geometry.
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![Elearning 279: Tangent circles](../problem/p279_tangent_circles_17.jpg) |
Proposed Problem
279.
Tangent Circles, Common External Tangent, Chords, Inradius. |
![Tangent Circles, Common External Tangent, Chord](../problem/p278_tangent_circles_17.jpg) |
Proposed Problem
278.
Tangent Circles, Common External Tangent, Chord. |
![Tangent Circles](../problem/p277_tangent_circles_17.jpg) |
Proposed Problem
277.
Tangent Circles, Common External Tangent. |
![Square, Circle, 90 Arc](../problem/p276_square_circle_17.jpg) |
Proposed Problem
276.
Square, 90 degree Arcs, Circle, Radius. |
![Sagitta Problem](../problem/p275_right_triangle_sagitta.jpg) |
Proposed Problem
275.
Right Triangle, Circumcircle, Sagitta, Inradius. |
![Sagitta, Arc, Chord](../circle/sagitta_chord_arc_17.jpg) |
Sagitta, Arc, Chord. |
![Bisect an angle](euclid_elements_book_i_9_17.jpg) |
Book I,
Proposition 9: Bisect a given angle
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![Isoscele triangle 80-80-20](../problem/p274_triangle_80_20_17.jpg) |
Proposed Problem
274.
Isosceles Triangle, 80-80-20, Angles. |
![Isosceles Triangle Index](isosceles_triangle_index_17.jpg) |
Isosceles Triangle. |
![Problem 273 Triangle and Squares](../problem/p273_triangle_square_17.jpg) |
Proposed Problem
273.
Triangle, Perpendiculars, Area of Squares. |
![Cube of the external common tangent](../problem/p272_tangent_circles_17.jpg) |
Proposed Problem
272.
Tangent Circles, the Cube of the Common external tangent. |
![Rhombus, Rhombuses, Rhombi](rhombus_index_17.jpg) |
Rhombus.
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![Cube of the external common tangent](../problem/p271_tangent_circles_17.jpg) |
Proposed Problem
271.
Tangent Circles, the Cube of the Common external tangent. |
![Heptagon index](heptagon_index_17.jpg) |
Heptagons. |
![Classical Theorems](http://gogeometry.com/
geometry/classical_theorems_17.jpg) |
Classical Theorems.
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Heptagon and Heptagrams / Septegram.
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Proposed Problem
270.
Tangent Circles, Common external tangent, Fractional exponents. |
![Circumcenter Index](../center/circumcenter_index_17.jpg) |
Circumcenter.
Index.
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![Pi: Irrational Math Constant](pi_314_math_17.jpg) |
Pi
Day.
Saturday, March 14, 2009 = 3.14
It's time to get irrational. Tomorrow is Pi Day, when mathematicians will gather to celebrate the mystery of science's most famous strange number. |
![Right triangle, Altitude, perpendiculars](../problem/p269_right_triangle_altitud.jpg) |
Proposed Problem
269.
Right Triangle, Altitude, Perpendicular, Projection. |
![Right triangle, Altitude, Catheti](../problem/p268_right_triangle_altitud.jpg) |
Proposed Problem
268.
Right Triangle, Catheti and Altitude. |
![Right triangle, Catheti product](../problem/p267_right_triangle_17.jpg) |
Proposed Problem
267.
Right Triangle, Product of Catheti. |
![Right triangle, Altitude, Geometric Mean](../problem/p266_right_triangle_17.jpg) |
Proposed Problem
266.
Right Triangle, Altitude, Geometric Mean. |
![Albert Einstein at the age of 12](../pythagoras/einstein_pythagoras_12_17.jpg) |
Albert Einstein
and the Pythagorean theorem.
A preteen Albert Einstein devised a new proof of the Pythagorean theorem. |
![Pythagorean Theorem](../problem/p265_pythagoras_theorem_17.jpg) |
Proposed Problem
265.
Right Triangle, Pythagorean Theorem. |
![Right triangle](../problem/p264_right_triangle_17.jpg) |
Proposed Problem
264.
Right Triangle, Altitude, Leg projection, Hypotenuse, Similarity, Geometric mean. |
![Problem 263: Triangle, Median Projection](../problem/p263_triangle_median_17.jpg) |
Proposed Problem
263.
Triangle, Median, Altitude, Orthogonal Projection, Sides. |
![Regular hexagon inscribed in a circle](../problem/p262_regular_hexagon_17.jpg) |
Proposed Problem
262.
Regular Hexagon inscribed in a circle, sum of distances. |
![Heaxagons](hexagon_polygon_index_17.jpg) |
Hexagons. |
![Regular pentagon inscribed](../problem/p261_regular_pentagon_17.jpg) |
Proposed Problem
261.
Regular Pentagon inscribed in a circle, sum of distances.
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![Pentagon Index](pentagon_polygon_index_17.jpg) |
Pentagons. |
![Orthocenter Index](../center/orthocenter_altitude_index.jpg) |
Orthocenter
Index.
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![Centroid of a triangle Index](../center/centroid_barycenter_index.jpg) |
Centroid
/Barycenter.
Index.
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![Elearning 260: Problem about equilateral triangle](../problem/p260_equilateral_triangle_1.jpg) |
Proposed Problem
260.
Equilateral Triangle, Incircle, Tangency Points, Vertices, Distances, Squares.
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![Elearning 259: Equilateral triangle, Incircle](../problem/p259_equilateral_triangle_1.jpg) |
Proposed Problem
259.
Equilateral Triangle, Incircle, Tangency Points, Side, Distances, Squares.
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![Elearning 258: Equilateral triangle, Incircle](../problem/p258_equilateral_triangle_1.jpg) |
Proposed Problem
258.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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![Problem 257: Equilateral triangle, circumcircle](../problem/p257_equilateral_triangle_1.jpg) |
Proposed Problem
257.
Equilateral Triangle, Circumcircle, Point, Vertices, Side, Distances,
Squares.
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![Elearning 256: Equilateral triangle](../problem/p256_equilateral_triangle_1.jpg) |
Proposed Problem
256.
Equilateral Triangle, Circumcircle, Point, Vertices, Distances.
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![Problem 254: Triangle and Centroid](../problem/p255_triangle_centroid_17.jpg) |
Proposed Problem
255.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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![Elearning 254: Triangle and Centroid](../problem/p254_triangle_centroid_17.jpg) |
Proposed Problem
254.
Triangle, Centroid, Vertices, a Point, Distances, Squares.
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![Elearning 253: Triangle, Centroid](../problem/p253_triangle_centroid_17.jpg) |
Proposed Problem
253.
Triangle, Centroid, Vertices, Distances, Squares.
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![Equilateral triangles](equilateral_triangle_17_ind.jpg) |
Equilateral Triangles Index. |
![Rectangle, Isosceles Right Triangle, Square, Area](../problem/p252_rectangle_area_17.jpg) |
Proposed Problem
252.
Rectangle, isosceles right triangle, square, area.
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![Elearning 251: Parallelogram](../problem/p251_parallelogram_area_17.jpg) |
Proposed Problem
251.
Parallelogram, sides, diagonals, squares, areas.
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![Quadrilateral, diagonals, midpoints](../problem/p250_quadrilateral_17.jpg) |
Proposed Problem
250.
Quadrilateral, sides, diagonals, midpoints, squares.
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![Triangle sides, medians, squares](../problem/p249_triangle_medians_17.jpg) |
Proposed Problem
249.
Triangle sides, medians, squares.
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![Median Length theorem](median_length_17.jpg) |
Median length, Apollonius' Theorem |
![Euclid's Elements, Book II, Proposition 12](euclid_elements_ii_12_17.jpg) |
Euclid's Elements Book II, Proposition 12: Law of Cosines.
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![Euclid's Elements: Book II, Proposition 13: Law of Cosines](euclid_elements_ii_13_17.jpg) |
Euclid's Elements Book II, Proposition 13: Law of Cosines.
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![Elearning: Napoleon Theorem III](../problem/p248_napoleon_theorem_17.jpg) |
Proposed Problem
248.
Napoleon's Theorem III. Inner and outer Napoleon triangles, Area.
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![Napoleon Theorem II](../problem/p247_napoleon_theorem_17.jpg) |
Proposed Problem
247.
Napoleon's Theorem II. Internal Equilateral triangles. Inner Napoleon
triangle.
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![Napoleon Theorem I](../problem/p246_napoleon_theorem_17.jpg) |
Proposed Problem
246.
Napoleon's Theorem I. External Equilateral triangles. |
![Elearning 245: Parallelogram](../problem/p245_parallelogram_equilate.jpg) |
Proposed Problem
245. Parallelogram with Equilateral triangles
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![Elearning 244: Square center, diagonal](../problem/p244_square_diagonal_17.jpg) |
Proposed Problem
244. Square, Diagonals, Centers, Distance.
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![Elearning 243](../problem/p243_equilateral_triangle_1.jpg) |
Proposed Problem
243. Triangle with Equilateral triangles, Parallelogram.
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![Elearn 242: Equilateral triangle and parallelogram](../problem/p242_equilateral_triangle_1.jpg) |
Proposed Problem
242. Triangle with Equilateral triangles, Parallelogram.
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![Equilateral triangle, congruence SAS](../problem/p241_equilateral_triangle_1.jpg) |
Proposed Problem
241. Triangle with Equilateral triangles, Congruence.
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![Triangle with equilateral triangles](../problem/p240_equilateral_triangle_1.jpg) |
Proposed Problem
240. Triangle with Equilateral triangles, Parallelogram.
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![Square, Midpoint, Congruence, Pythagoras](http://gogeometry.com/
problem/p239_square_midpoint_17.jpg) |
Proposed Problem
239. Square, Midpoints, Lines, Congruence, Pythagoras.
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![Square. Midpoint, Congruence](http://gogeometry.com/
problem/p238_square_midpoint_17.jpg) |
Proposed Problem
238. Square, Midpoints, Lines, Congruence.
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![Quadrilateral, midpoints](http://gogeometry.com/
problem/p237_quadrilateral_17.jpg) |
Proposed Problem
237. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.
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![Quadrilateral, midpoints](http://gogeometry.com/
problem/p236_quadrilateral_17.jpg) |
Proposed Problem
236. Quadrilateral, Midpoints, Exterior line, Perpendicular lines.
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![Problem about Parallelogram and transversal](http://gogeometry.com/
problem/p235_parallelogram_17.jpg) |
Proposed Problem
235. Parallelogram, Transversal line, Perpendicular lines.
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![Problem 233: Parallelogram](http://gogeometry.com/
problem/p234_parallelogram_17.jpg) |
Proposed Problem
234. Parallelogram, Line through a vertex, Perpendicular lines.
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![Elearn 232: Parallelogram](http://gogeometry.com/
problem/p233_parallelogram_17.jpg) |
Proposed Problem
233. Parallelogram, Exterior line, Perpendicular lines.
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![Parallelograms Index](http://gogeometry.com/
geometry/parallelograms_17.jpg) |
Parallelograms
Index.
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![Elearn 232: Parallelogram, perpendicular lines](http://gogeometry.com/
problem/p232_parallelogram_problem_.jpg) |
Proposed Problem
232. Parallelogram, Line through a vertex, Perpendicular lines.
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![Geometry terms](http://gogeometry.com/
glossary_terms/geometry_glossary_17.jpg) |
Geometry Online
Glossary .
Geometry Glossary based on the new New York State
mathematics standards initiative. |
![Elearn 231: Triangle, Midpoint](http://gogeometry.com/
problem/p231_triangle_midpoint_17.jpg) |
Proposed Problem
231. Triangle, Midpoints, Transversal, Perpendicular lines.
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![Elearn 230: Triangle, Midpoint, Transversal](http://gogeometry.com/
problem/p230_triangle_midpoint_17.jpg) |
Proposed Problem
230. Triangle, Midpoints, Transversal, Perpendicular lines.
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![Elearn 229: Triangle, Centroid, Transversal](http://gogeometry.com/
problem/p229_triangle_centroid_17.jpg) |
Proposed Problem
229. Triangle, Centroid, Transversal, Perpendicular lines. |
![Elearn 228: Triangle, Midpoint](http://gogeometry.com/
problem/p228_triangle_midpoint_17.jpg) |
Proposed Problem
228. Triangle, Midpoints, Exterior line, Perpendiculars lines.
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![Elearn 227: Triangle, Centroid](http://gogeometry.com/
problem/p227_triangle_centroid_17.jpg) |
Proposed Problem
227. Triangle, Centroid, Exterior line, Perpendicular lines. |
![Problem 226: Triangle, Centroid](http://gogeometry.com/
problem/p226_triangle_centroid_17.jpg) |
Proposed Problem
226. Triangle, Centroid, Perpendicular lines. |
![Viviani theorem extension, regular polygon](http://gogeometry.com/
problem/p225_viviani_theorem_17.jpg) |
Proposed Problem 225. Viviani's Theorem Extension, Regular Polygon,
Apothem, Distance. |
![Viviani theorem, isosceles triangle, extension on the base](http://gogeometry.com/
problem/p224_viviani_theorem_17.jpg) |
Proposed Problem 224. Viviani's theorem, Isosceles triangle,
Altitude, Distances, Point on the extension of the base. |
![Viviani theorem, Isosceles triangle](http://gogeometry.com/
problem/p223_viviani_theorem_17.jpg) |
Proposed Problem 223. Viviani's theorem, Isosceles triangle,
Altitude, Distances. |
![Viviani theorem, Equilateral triangle, exterior point](http://gogeometry.com/
problem/p222_viviani_theorem_17.jpg) |
Proposed Problem 222. Viviani's theorem, Equilateral triangle,
Exterior point, Distances. |
![Viviani's theorem I](http://gogeometry.com/
problem/p221_viviani_theorem_17.jpg) |
Proposed Problem 221. Viviani's theorem, Equilateral triangle,
Interior point, Distances. |
![Lune of Hippocrates Index](http://gogeometry.com/geometry/lune_hippocrates_index_17.jpg) |
Lune of Hippocrates Index.
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![Right triangle, inradius, altitude, arithmetic mean](http://gogeometry.com/problem/p220_right_triangle_17.jpg) |
Proposed Problem 220. Right Triangle, Altitude, Angle Bisector,
Distance, Arithmetic Mean.
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![Rhombus problem](http://gogeometry.com/
problem/p219_rhombus_mean_17.jpg) |
Proposed Problem 219. Rhombus, perpendiculars, arithmetic mean.
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![Elearn 218: Right triangle](http://gogeometry.com/
problem/p218_right_triangle_17.jpg) |
Proposed Problem 218. Right triangle, Altitude and Projections.
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![Elearn 217: Right triangle, Altitude, Projections](http://gogeometry.com/
problem/p217_right_triangle_17.jpg) |
Proposed Problem 217. Right triangle, Altitude and Projections.
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![Elearn: Quadrilateral, Angle Bisectors, Concurrency](http://gogeometry.com/
problem/p216_quadrilateral_concurre.jpg) |
Proposed Problem 216. Quadrilateral, Angle Bisectors, and
Concurrency.
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![Elearn 215: Cyclic quadrilateral](http://gogeometry.com/
problem/p215_quadrilateral_cyclic.jpg) |
Proposed Problem 215.
Quadrilateral, Angle Bisectors, and Cyclic
Quadrilateral.
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![Elearn 214](http://gogeometry.com/
problem/p214_quadrilateral_problem.jpg) |
Proposed Problem 214.
Quadrilateral and Angle Bisectors.
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![Elearn 213 Triangle Inradius, Common Tangents](http://gogeometry.com/
problem/p213_triangle_circle_170.jpg) |
Proposed Problem 213. Triangle, Incircle, Inradius, Semicircles,
Common Tangents. |
![Elearn 212: 120 degree triangle, area](http://gogeometry.com/
problem/p212_triangle_120_area_17.jpg) |
Proposed Problem 212. 120 Degree Triangle, Equilateral triangles,
Areas.
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![Archimedes Arbelos and Square](http://gogeometry.com/
geometry/arbelos_circle_square_2_17.jpg) |
Archimedes Arbelos and Square 2.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
![Archimedes Arbelos and Square](http://gogeometry.com/
geometry/arbelos_circle_square_17.jpg) |
Archimedes Arbelos and Square 1.
Dynamic Geometry Software.
Step-by-Step construction, Manipulation, and animation. |
![Elearn 211: 60 degree triangle, area](http://gogeometry.com/
problem/p211_triangle_60_area_17.jpg) |
Proposed Problem 211. 60 Degree Triangle, Equilateral triangles,
Areas.
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![Elearn 210](http://gogeometry.com/
problem/p210_triangle_angles_17.jpg) |
Proposed Problem 210. Triangle, Angles, Auxiliary Lines.
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![Elearn 209](http://gogeometry.com/
problem/p209_triangle_incircles_17.jpg) |
Proposed Problem
209. Triangle, Incircles, Inradius. |
![Clifford's theorem](http://gogeometry.com/
geometry/clifford_theorem_17.jpg) |
Clifford's Circle Chain
Theorems. This is a step by step presentation of the first theorem.
Clifford discovered, in the ordinary Euclidean plane, a "sequence or
chain of theorems" of increasing complexity, each building on the last
in a natural progression.
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![Elearn 208: Triangle, Angles](http://gogeometry.com/
problem/p208_triangle_angles_17.jpg) |
Proposed Problem
208. Triangle, Excircles, Angles, 360 degrees. |
![Problem 207: Hypotenuse](http://gogeometry.com/
problem/p207_right_triangle_hypoten.jpg) |
Proposed Problem
207. Right Triangle, Hypotenuse, Inradius, Exradius relative to the hypotenuse. |
![Elearn 206](http://gogeometry.com/
problem/p206_right_triangle_area_17.jpg) |
Problem 206. Area of a Right Triangle, Inradius, and Exradius relative to the hypotenuse. |
![Right triangle area](http://gogeometry.com/
problem/p205_right_triangle_area_17.jpg) |
Proposed Problem
205. Right Triangle Area, Exradii relatives to legs or catheti. |
![Elearn 204](http://gogeometry.com/
problem/p204_right_triangle_circle_.jpg) |
Proposed Problem
204. Right Triangle, Incircle, Excircles, Inradius, Exradii. |
![Problem 203](http://gogeometry.com/
problem/p203_right_triangle_circle_.jpg) |
Proposed Problem
203. Right Triangle, Excircles, Exradii, Hypotenuse. |
![Problem 202 Right triangle, excircles](http://gogeometry.com/
problem/p202_right_triangle_circle_.jpg) |
Proposed Problem
202. Right Triangle, Incicrle, Excircles relatives to catheti, Points of Tangency, Exradius, Semiperimeter. |
![Elearn 201](../problem/p201_right_triangle_17.jpg) |
Proposed Problem
201. Right Triangle, Excircles, Points of Tangency, Exradius, Semiperimeter. |
![Elearning 200: Right Triangle](../problem/p200_right_triangle_17.jpg) |
Proposed Problem
200. Right Triangle, Incircle, Excircles, Points of Tangency, Inradius. |
![Problem: Triangle, Altitude, Angles](../problem/p199_triangle_angle_17.jpg) |
Proposed Problem 199. Triangle, Quadrilateral, Angles.
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![Geometry problem about angles and triangle](../problem/p198_quadrilateral_angle_17.jpg) |
Proposed Problem
198. Triangle, Quadrilateral, Angles.
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![Elearning 197: Triangle Area](../problem/p197_area_triangle_radius_1.jpg) |
Proposed Problem
197. Area of a Triangle, Side, Inradius, and Exradius. |
![Elearning 196: Inradius, Exradii](../problem/p196_triangle_radius_17.jpg) |
Proposed Problem
196. Triangle, Inradius and Exradii Formula. |
![](../triangle_center_170.jpg) |
Triangle Centers Index. |
![Geometry: Triangle Area, inradius, exradii](../problem/p195_area_triangle_radius_1.jpg) |
Proposed Problem
195. Area of a Triangle, Inradius, Exradii. |
![Area of a triangle, semiperimeter, exradius](../problem/p194_area_triangle_exradius.jpg) |
Proposed Problem
194. Area of a Triangle, Semiperimeter, Exradius. |
![Area of a triangle, semiperimeter, inradius](../problem/p193_area_triangle_inradius.jpg) |
Proposed Problem
193. Area of a Triangle, Semiperimeter, Inradius. |
![Geometry Problem Circle, Diameter, and Chord](../problem/p192_circle_diameter_chord_.jpg) |
Proposed Problem
192. Circle, Diameter, Chord, Perpendicular, Triangle, Area.
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![Geometry Problem 191 about triangle and squares](../problem/p191_triangle_square_17.jpg) |
Proposed Problem
191. Triangle, Altitudes, Orthocenter, Squares, Areas.
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