This Semicircle Trick Works for ANY Triangle
Semicircle inscribed in a 5-12-13 right triangle — can you find the area?
In this video, I solve a classic geometry problem step by step. We have a right triangle with sides 5, 12, and 13. A semicircle is inscribed inside, touching both legs.
Your challenge — find the area of that semicircle. Try it yourself before watching. I promise it feels ten times more satisfying when you attempt it first.
What you will learn in this video:
— How the tangent-radius theorem creates a hidden perfect square
— How to split the triangle into three simple pieces
— How to build and solve one clean equation for the radius
— How to calculate the final area of the semicircle
Final Answer: Area = 19.55 square units
This trick works for any inscribed semicircle problem — once you see it, you will never forget it.
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Timestamps
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0:00 — The square nobody notices
0:28 — Understanding the diagram
1:33 — Tangent-radius theorem explained
2:18 — Splitting triangle into three parts
3:15 — Area of the big triangle
4:05 — Setting up the equation
4:35 — Solving for radius — r = 60/17
5:30 — Calculating the final area
5:45 — Final answer — 19.55 sq units
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Who is this for?
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— Students preparing for GCSE, SAT, or any geometry exam
— Anyone who enjoys satisfying math problems
— Teachers looking for a clean visual explanation
— Anyone who wants to think smarter, not harder
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If this helped you, please LIKE the video — it takes one second and helps more students find this content. SUBSCRIBE for a new problem every week. And drop a COMMENT — could you spot the hidden square before I revealed it? I read every single one.
Thanks so much for watching — see you in the next one!
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