The Genius Formula to Find the Area of a Circle Inside Any Triangle

Ever wondered how to find the area of a circle inscribed in a triangle—whether it's a right triangle, scalene, or even equilateral? In this video, we dive deep into a powerful yet simple formula that unlocks the radius and area of an incircle using only triangle side lengths. 📐

We’ll break down:

The shortcut formula for incircle radius:
𝑟=𝐴/𝑠

How to apply it to both right and non-right triangles

Step-by-step examples using 45-45-90, 3-4-5, and 9-12-15 triangles

Bonus challenge problems to test your skills!

Whether you're a student preparing for a math exam or a curious problem solver, this is a must-know concept that shows up in geometry competitions and entrance exams.

📌 Timestamps:
0:00 Intro & Problem Setup
0:28 Formula for Incircle Radius
1:45 Solving with Isosceles Right Triangle
3:35 Simplifying with Conjugates
5:00 Example with 3-4-5 Triangle
6:15 Challenge Problem 1: 9-12 Right Triangle
7:00 Challenge Problem 2: Scalene Triangle (Heron’s Formula)
8:00 Wrap-Up & Final Thoughts

👇 Drop your answers to the challenge problems in the comments below. Let’s discuss different approaches!

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