Geometric Challenge Problem 1614 - Area Equivalence in a Semicircle with Inscribed Rectangles, Synthetic Geometry.

Geometry Challenge 1614: Share your proof or solution in the comments below.
Target Audience: K-12, Honors Geometry, and College Mathematics Education.

Explore the full theorem and interactive diagrams by clicking the illustration below.

Click for additional details.

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!

Ready to contribute?
Please use the box below to Enter your Comment or Solution. You can use plain text or provide links to your diagrams.

Geometry Problem 1601: Rectangular Property of Cyclic Orthodiagonal Quadrilaterals

Challenging Geometry Puzzle: Problem 1601. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

Gain comprehensive insights! Click below to reveal the complete details and interactive version.

Click for additional details.

Share your solution by clicking 'Comment' below the post or entering your solution or comment in the 'Enter Comment' field and pressing 'Publish'.

Geometry Problem 1595: Prove that the total field area is determined by three key zones: A1, A2, A3

Challenging Geometry Puzzle: Problem 1595. Share your solution by posting it in the comment box provided.
Audience: Mathematics Education - K-12 Schools, Honors Geometry, and College Level.

Gain comprehensive insights! Click below to reveal the complete details.

Click for additional details.

Share your solution by clicking 'Comment' below the post or entering your solution or comment in the 'Enter Comment' field and pressing 'Publish'.

Geometry Problem 1530: Unlock the Secrets of Geometric Angles: Calculate the Measurement of an Angle in a Square and Rectangle Figure Today

Geometry Problem 1530. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

More Details

To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

Geometry Problem 1523: Discover How to Calculate the Length of the Altitude in an Isosceles Triangle

Geometry Problem 1523. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

More Details

To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

Geometry Problem 1520: Discovering Distances in a Rectangle with an Exterior Point: A Geometry Challenge. Difficulty Level: High School.

Geometry Problem 1520. Post your solution in the comment box below.
Level: Mathematics Education, K-12 School, Honors Geometry, College.

Details: Click on the figure below.

More Details

To post a solution to this problem click Comment underneath the post, or click into the line that says, “Enter Comment.” Type what you want to say and press Publish to post your solution.

Geometry Problem 1472: Cyclic Quadrilateral, Perpendicular Diagonals, Rectangle

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.

Zoom

Geometry Problem 1467: Square, Rectangle, Triangle, Area

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

Details: Click on the figure below.

Zoom

Dynamic Geometry 1452: Japanese Theorem, Sangaku

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.

Zoom

Geometry Problem 1439: Rectangle, Diagonal, Perpendicular, Circles, Areas

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

Details: Click on the figure below.

Zoom

Geometry: Ptolemy's Theorem: Cyclic Quadrilateral

Geometric Art: Typography, iPad

Details: Click on the figure below.

Zoom

Geometry Problem 1400: Triangle with three rectangles on the sides, Perpendicular Bisectors, Concurrency

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

Details: Click on the figure below.

Zoom

Geometry Problem 1396: Triangle with three rectangles on the sides, Vertices, Perpendicular lines, Concurrency

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

Details: Click on the figure below.

Zoom

Geometry Problem 1395: Triangle with three rectangles on the sides, Midpoints, Perpendicular lines, Concurrency

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

Details: Click on the figure below.

Zoom

Typography of Geometry Problem 866: Cyclic Quadrilateral, Circle, Rectangle, Center, Congruence, 90 Degrees, iPad Apps

Geometric Art: Typography, iPad

Details: Click on the figure below.

Zoom

Geometry Problem 868: Cyclic Quadrilateral, Circle, Five Rectangles, Four Centers, Congruence, Typography, iPad Apps

Geometric Art: Typography, iPad

Details: Click on the figure below.

Zoom

Geometry Problem 1352: Rectangles, Sum of Squared Distances

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

Details: Click on the figure below.

Zoom

Geometry Problem 1318: Rectangle, Equilateral Triangle, Distances, Perpendicular, Measurement

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

Details: Click on the figure below.

Zoom

Geometry in Venetia Diamond Mine, Limpopo, South Africa, Square, Rectangle Shapes

Geometry in the Real World
Click the figure below to view the interactive satellite map.

Zoom

Geometry Problem 1198: Right Triangle, Square, Rectangle, Quadrilateral, Altitude, Equal Areas

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

Click the figure below to view more details of problem 1198.

Zoom