Geometry Problems - Table of Content (Page 1 of 6)
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Problem 517.
Right Triangle, Six Squares, Areas.

Problem 516.
Triangle, Cevian, Congruence, Angles.

Problem 515.
Triangle, Double Angle, Altitude, Measure.

Problem 514.
Triangle, Five Squares, Line, Area.

Problem 513.
Triangle, Double Angle, Exterior Angle Bisector, Measure.

Problem 512.
Triangle with three squares and concurrency.

Problem 511.
Triangle, Double Angle, Angle Bisector, Measure.

Problem 510.
Triangle, Three Squares, Midpoints, Concurrency.

Problem 509.
Triangle, 120 Degrees, Angles, Congruence, Mind Map.

Problem 508.
Triangle with three Squares, Four triangle of equal Area.

Problem 507.
Triangle, Interior Point, 120 Degrees, Congruence, Angle.

Problem 506.
Triangle with Three Squares, Center, Midpoint, Perpendicular.

Problem 505.
Right Triangle, Cevian, Sum of Segments, Angles.

Problem 504.
Equilateral Triangle, Angles, 45, 60 Degrees.

Problem 503.
Triangle with Three Squares, Perpendicular, Congruence, Concurrency.

Problem 502.
Triangle, Two Squares, Midpoint, Perpendicular, Half the measure.

Problem 501.
Triangle, Two Squares, Center, Midpoint, another Square.

Problem 500.
Circle, Diameter, Chord, Perpendicular, Measure.

Problem 499.
Triangle, Two Squares, Perpendicular.

Problem 498.
Triangle, Angle Bisector, Double Angle, Measure.

Problem 497.
Triangle, Two Squares, Centers, Midpoint, 90 Degrees.

Problem 496.
Triangle, Two Squares, 90 Degrees, Concurrency, Angle Bisectors.

Problem 495.
Triangle, 120 Degrees, Angle Bisectors.

Problem 494.
Circular Sector, 90 Degrees, Semicircle, Chord, Parallel.

Problem 493.
Right Triangle, Circumcircle, Perpendicular, Chord.

Problem 492.
Cyclic Quadrilateral, Circle, Perpendicular, Side, Diagonal, Parallel.

Problem 491.
Square, Right Triangle, Incircle, Inscribed Circle, Radius.

Problem 490.
Tangent Circles, Arc, Radius, Circular Sector, Area.

Problem 489.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle.

Problem 487.
Intersecting Circles, Area, Diameter, Parallel, 90 Degrees.

Problem 486.
Tangent circles, Chord, Arc, Midpoint, Collinearity, Congruence.

Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement.

Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion.

Problem 483.
Square, Angle, 90 degrees, Measurement.

Problem 482.
Triangle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic Points.

Problem 481.
Triangle, Altitude, Cevian, Perpendicular, Angle.

Problem 480.
Triangle, Circle, Center, Altitude, Angle, Circumcenter.

Problem 479.
Triangle, Cevians, Concurrency, Transversal, Proportion.

Problem 478.
Triangle, Sides, Circumradius, Circumcenter, Circumcircle.

Problem 477.
Parallelogram, Triangle, Quadrilateral, Area.

Problem 476.
Triangle, Circumcenter, Circumcircle, Angles.

Problem 475.
Tangent Circles, Secant, Tangent, Parallel.

Problem 474.
Parallelogram, Diagonal, Circle, Vertex.

Problem 473.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Problem 472.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Problem 471.
Triangle, Parallel, Side, Concurrency, Area, Similarity.

Problem 470.
Triangle, Parallel, Side, Parallelogram, Area, Similarity.

Problem 469.
Isosceles triangle, Midpoint, Transversal, Congruence.

Problem 468.
Circle, Chord, Midpoint, Congruence, Angle.

Problem 467.
Concentric Circles, Chord, Tangent, Congruence, Measurement.

Proposed Problem 466.
Concentric Circles, Secant, Congruence, Measurement.

Proposed Problem 465.
Square, Arc, Angle, 90 Degrees, Measurement.

Proposed Problem 464.
Square, Arcs, Center, Angle, 90 Degrees, 120 Degrees.

Proposed Problem 463.
Three Concentric Circles, Secant, Tangent, Triangle, Area.

Proposed Problem 462.
Square, Arcs, 90 Degrees, Circle, Tangent, Radius, Measurement.

Proposed Problem 461.
Three Circles, Tangent, Right Angle, Center, Distance, Measurement.

Proposed Problem 460.
Circle, Tangent, Perpendicular, Radius, Distance, Measurement.

Proposed Problem 459.
Right triangle, Squares, Distance, Measurement.

Proposed Problem 458.
Square, Semicircle, Circular Sector, Internal Common Tangent, Measurement.

Proposed Problem 457.
Triangle, First Brocard Point, Congruent angles, Circle, Circumradius.

Proposed Problem 456.
Three tangent circles, Center, Chord, Secant, Collinear.

Proposed Problem 455.
Rhombus, Inscribed Circle, Angle, Chord, 45 Degrees.

Proposed Problem 454.
Triangle, Incircle, Inradius, Tangent, Circle, Radius.

Proposed Problem 453.
Intersecting Circles, Tangent, Circular Segment, Congruence, Area.

Proposed Problem 452.
Triangle, Circle, Tangent, Proportional Segments.

Proposed Problem 451.
Triangle, Median, Congruence, Proportional Segments.

Proposed Problem 450.
Triangle, Median, Cevian, Congruence, Proportional Segments.

Proposed Problem 449.
Congruent Tangent Circles, Diameter, Sagitta, Arc, Perpendicular, Chord.

Proposed Problem 448.
Tangent Circles, Diameter, Perpendicular, Chord.

Proposed Problem 447.
Complete Quadrilateral, Inradii, Exradii, Sides.

Proposed Problem 446.
Quadrilateral Area, Dividing the sides into 5 equal parts.

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Proposed Problem 445.
Three Tangent Circles, Tangency Points, Circumradius.

Proposed Problem 444.
Internally Tangent circles, Secant line, Chords, Angles, Congruence.

Proposed Problem 443.
Overlapping, Intersecting Circles, Common Chord, Secant line, Tangent line, Angles.

Proposed Problem 442.
Triangle, Median, Cevian, Transversal, Congruent Angles.

Proposed Problem 441.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Proposed Problem 440.
Triangle, Incircle, Incenter, Angle Bisector, Tangency Points, Circle, Angles.

Proposed Problem 439.
Isosceles triangle, Cevian, Incenter, Angles, Circle.

Proposed Problem 438.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement, Parallel lines.

Proposed Problem 437.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Proposed Problem 436.
Tangent Circles, Diameter, Chord, Perpendicular, Congruence, Measurement.

Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.

Proposed Problem 435.
Triangle, Incircle, Inradius, Congruent circles, tangent, Measurement.

Proposed Problem 434.
Quadrilateral, Transversal, Ratio, Measurement, Similarity.

Proposed Problem 433.
Quadrilateral, Triangle, Area, Proportion, Measurement, Similarity.

Proposed Problem 432.
Trapezoid, Parallel, Measurement, Similarity, Transversal.

Proposed Problem 431.
Quadrilateral, Midpoints of Diagonals, Transversal.

Proposed Problem 430.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Areas.

Proposed Problem 429.
Circumscribed and Inscribed Regular Pentagon, Perpendicular, Measurement.

Proposed Problem 428.
Quadrant of a circle, Square, Angle bisector, Measurement.

Proposed Problem 427.
Triangle, Two Altitudes, Square of a Side.

Euclid's Elements Book I, Proposition 5: (Pons Asinorum) Isosceles triangles

Euclid's Elements Book I, Proposition 6: Converse of I.5
"Proof by contradiction," also called reductio ad absurdum.

Proposed Problem 426.
Triangle, Circumradius, Circumcenter, concurrent Cevians.

Euclid's Elements Book I, Proposition 4: (Side-Angle-Side SAS)

Proposed Problem 425.
Quadrilateral, Triangle, Angles, 10, 20, 50 degrees, Congruence.

Proposed Problem 424.
Triangle, Cevian, Angle, 90 degree, Congruence.

Proposed Problem 423.
Triangle, 30, 40 degree, Angle, Congruence.

Proposed Problem 422.
Triangle, 24, 30 degree, Angle, Congruence.

Proposed Problem 421.
Right Triangle, Cevian, Angles, Measurement.

Euclid's Elements Book I, Proposition 3: Given two unequal straight lines, to cut off from the greater a straight line equal to the less

Euclid's Elements Book I, Proposition 2: To place at a given point (as an extremity) a straight line equal to a given straight line

Euclid's Elements Book I, Proposition 1: On a given finite line to construct an equilateral triangle

Proposed Problem 420.
Triangle, Altitude, Angles, Sides, Measurement.

Proposed Problem 419.
Triangle, Cevian, Incircle, Excircle, Inradius, Exradius.

Proposed Problem 418.
Triangle, Incircle, Inradius, Equal Tangent circles, Radius.

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Computational, Manifold, Topology, String theory, Coordinate, Analytical, Trigonometry, Projective, Algebraic, Differential, Symplectic, Lie theory, Fractal, Dimension theory, Computer graphics, Atiyah, Gromov, Perelman.

Proposed Problem 417.
Tangent circles, Tangent lines, Angles.

Routh's Theorem 1.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 2.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 3.
Triangle, Cevians, Ratio of Areas.

Routh's Theorem 4.
Triangle, Cevians, Ratio of Areas.

Proposed Problem 416.
Triangle, Cevians, Trisectors, Area.

Proposed Problem 415.
Right Triangle, Cevian, Angles, Congruence.

Proposed Problem 414.
Triangle, Angles, Altitude, Median, Congruence.

Proposed Problem 413.
Cyclic Quadrilateral, Orthocenter, Parallelogram, Concurrency, Congruence.

Proposed Problem 412.
Triangle, Cevian, Angles, Congruence.

Proposed Problem 411.
Triangle, Median, Angles.

Proposed Problem 410.
Two Regular Pentagons, Angle.
Puzzle: 22 piece polygons.

Proposed Problem 409.
Quadrilateral, Diagonals, Perpendicular, Congruence.

Proposed Problem 408.
Cyclic quadrilateral, Perpendicular, Parallelogram, Congruence.

Proposed Problem 407.
Circle, Angle, Tangent, Perpendicular, Secant, Radius, Center.

Proposed Problem 406.
Right triangle, 15 degrees, Midpoints, Congruence.

Proposed Problem 405.
Quadrilateral, 60, 75, and 135 degrees, Midpoint.

Proposed Problem 404.
External Equilateral triangles, Congruent and Concurrent Lines.

Proposed Problem 403.
Circular sector, 90 degrees, Circle, Semicircle, Area.

Proposed Problem 402.
Hexagon, Triangle, Centroid, Parallel, Congruence, Similarity.

Proposed Problem 401.
Area, Triangle, Angle bisector, Circumcircle, Perpendicular bisector, Congruence.
Puzzle based on poblem 401.

Proposed Problem 400.
Triangle, Angle bisector, Circumcircle, Perpendicular, Congruence.

Proposed Problem 399.
Right triangle, Midpoints, Distance, Pythagorean theorem, Congruence.

Proposed Problem 398.
Parallelogram, Area, Similarity, Congruence.

Proposed Problem 397.
Triangle, Altitude, Midpoints, Congruence.

Proposed Problem 396.
Square, Angle Trisectors, Congruence, Area.

Proposed Problem 395.
Square, 15 Degree, Equilateral triangle.

Proposed Problem 394.
Square, 90 Degree Arc, Diagonal, Congruence.

Proposed Problem 393.
Triangle, Orthocenter, Circumcircles, Congruence, Collinear.

Proposed Problem 392.
Triangle, Parallel lines, Concurrent lines.

Proposed Problem 391.
Triangle, Parallel lines, Collinear points.

Proposed Problem 390.
Triangle, Parallel lines, Collinear points.

Proposed Problem 389.
Triangle, Parallel lines, Harmonic Mean.

Proposed Problem 388.
Triangle, Angle bisector, Perpendicular, Parallel.

Proposed Problem 387.
Triangle, Angle bisector, Perpendicular, Concyclic points.

Proposed Problem 386.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter, Congruence.

Proposed Problem 385.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Proposed Problem 384.
Triangle, Angle bisector, Perpendicular, Parallel, Semiperimeter.

Proposed Problem 383.
Concave Quadrilateral, Angle Bisectors, Semi-difference of Angles.

Proposed Problem 382.
Concave Quadrilateral, Angle Bisectors, Semi-sum of Angles.

Proposed Problem 381.
Quadrilateral, Diagonals, Angle Bisectors, Semi-sum of Angles.

Proposed Problem 380.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 379.
Triangle, Excenter, Parallel to a side, Angle, Congruence.

Proposed Problem 378.
Triangle, Incenter, Parallel to a side, Angle, Congruence.

Proposed Problem 377.
Triangle, Internal Angle Bisector, Altitude.

Proposed Problem 376.
Triangle, Excenter, Internal and External Angle Bisectors.

Proposed Problem 375.
Triangle, Excenter, External Angle Bisectors.

Proposed Problem 374.
Triangle, Incenter, Internal Angle Bisectors.

Proposed Problem 373.
Square, Inscribed Circle, Diagonal, Perpendicular, Angle.

Proposed Problem 372.
Circles, Common Internal and External Tangent, Angles.

SAT Math Practice 1,
Video.

Proposed Problem 371.
Square, Inscribed circle, Triangle, Area.

Mind Map of How to Solve Problems
George Pólya's 1945 book How to Solve It is a book describing methods of problem solving.