Uploaded March 2025 | Updated September 2026, 2 weeks ago

---

Solving a geometry puzzle from Archimedes Lab, concerning a square with a vertex on a circle inscribed in a semicircle. It is our challenge to express the area of the square in terms of the diameter of the semicircle without the use of trigonometry. We'll need the angle bisector theorem and several other basic results to solve this geometry problem. #maths #mathproblems #geometry

Join Wrath of Math to get exclusive videos, lecture notes, and more:
youtube.com/channel/UCyEKvaxi8mt9FMc62MHcliw/join

More math chats: youtube.com/playlist?list=PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO

Original Puzzle: archimedes-lab.org/monthly_puzzles_76.html

★DONATE★
◆ Support Wrath of Math on Patreon:
patreon.com/join/wrathofmathlessons
◆ Donate on PayPal: paypal.me/wrathofmath

Follow Wrath of Math on...
● Instagram: instagram.com/wrathofmathedu
● TikTok: tiktok.com/@wrathofmathedu
● X: https://x.com/wrathofmathedu

0:00 Intro
1:24 Hints
2:05 Solution Start
4:59 Beginning Assertions
5:52 Angle Bisector Theorem
8:08 Similar Triangles
9:51 Pythagorean Theorem
14:11 Finding the Area
15:27 Conclusion