Geometric Challenge Geometry Problem 1617: The Concyclic Hexagon and the Power of Intersecting Circumcircles

Share your proof or solution in the comments below.
Target Audience: K-12, Honors Geometry, and College Mathematics Education.

Discover the hidden symmetry of intersecting systems in Problem 1617. This challenge moves away from simple tangency to explore a more complex configuration where two circles overlap, creating a remarkable "Concyclic Hexagon."
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Proposed Solution
We invite students, teachers, and enthusiasts to share their proofs. This classic challenge can be approached using synthetic geometry.

How to contribute:
Post your step-by-step proof in the comments below. Feel free to:

• Describe your construction and properties applied (centroid/medians).
• Provide a link to a diagram (GeoGebra, Desmos, etc.) if you have one.

Be the first to submit a formal solution!

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Geometry Problem 1604: Can You Find FG?

Challenging Geometry Problem 1604. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometry Problem 1560: Trapezoid ABCD

Challenging Geometry Puzzle: Problem 1560. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometry Problem 1555: Find Length of DE

Challenging Geometry Puzzle: Problem 1555. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

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Geometry Problem 1540: Solving for the Length of Chord in a Circle: Analyzing Intersections and Given Values

Geometry Problem 1540. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

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Geometry Problem 1500: Circle, Perpendicular, Tangent, Secant, Cyclic Quadrilateral, Parallel, Similarity, Measurement

Geometry Problem 1500. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

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More Details

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Geometry Problem 1457: Altitudes, Circles, Similarity, Product of the Inradii Lengths

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1456: Altitudes, Orthic Triangle, Circumcircle, Parallel, Similarity, Area

Interactive step-by-step animation using GeoGebra. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

Details: Click on the figure below.

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Geometry Problem 1442 Triangle, Altitudes, Orthocenter, Perpendicular, Congruent Angles, Similarity, Measurement, iPad apps

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1432: Tangent Circles, Secant, Tangent Lines, Proportionality, Similarity

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1386: Thabit ibn Qurra Theorem, generalized Pythagorean Theorem

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometric Art: Problems 21-30, Triangle, Angles, Circle, Congruence, Similarity, Auxiliary Lines, Typography, iPad Apps

Geometric Art: Typography, iPad

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Typography of Geometry Problem 63: Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity, iPad Apps

Geometric Art: Typography, iPad

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Typography of Geometry Problem 865: Parallelogram, Diagonal, Midpoint, Side, Triangle, Parallel, Similarity, iPad Apps

Geometric Art: Typography, iPad

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Typography of Geometry Problem 834: Parallelogram, Diagonal, Similarity, Geometric Mean, iPad Apps

Geometric Art: Typography, iPad

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Geometry Problem 1185: Similar Rectangles, Four Quadrilaterals, Sum of Areas, Metric Relations

Geometry Problem. Post your solution in the comment box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1173: Triangle, Cevian, Angle, Congruence, Similarity

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1172: Cyclic Quadrilateral, Circle, Secant, Triangle, Similarity, Metric Relations

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1135: Intersecting Circles, Secant, Parallel Line, 90 Degrees, Similar Triangles

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Geometry Problem 1133: Circle, Chord, Tangent, Circumcircle, Similarity, Equal Product

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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