Monday, July 13, 2026

Geometric Challenge

1620 Problem: Perpendicular Chords and Circle Area Invariant

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

Two perpendicular chords partition a circle of radius R into four consecutive regions. Prove that the sum of the areas of non-adjacent regions is invariant.
Explore the full theorem and illustrated diagrams by clicking the image below.

Illustration of Geometry Problem 1620: Perpendicular Chords and Circle Area Invariant
Click for additional details and full diagram.

Proposed Solution
We invite students, teachers, and math enthusiasts to share their insights using synthetic geometry or classical circle properties.

How to contribute:
Post your step-by-step proof in the comments below:
  • Describe the theorems applied.
  • Share a link to your dynamic construction (GeoGebra, Desmos).
Be the first to submit a formal solution for this problem!
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