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Home » This Is Why Fans Are Goalgazing Over Grace Morris’s Latest Phenomenal Comeback! - Esdistancia

This Is Why Fans Are Goalgazing Over Grace Morris’s Latest Phenomenal Comeback! - Esdistancia

📅 March 17, 2026 👤 scraface

Mar 17, 2026

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📌 #### 30000Question: In a right triangle, the radius of the inscribed circle is $ r $, and the hypotenuse is $ h $. If the two legs are in the ratio $ 3:4 $, find the ratio of the area of the circle to the area of the triangle in terms of $ r $.

📌 Let the legs of the right triangle be $ 3k $ and $ 4k $, so the hypotenuse is $ h = 5k $ by the Pythagorean theorem.

📌 The inradius $ r $ of a right triangle is given by the formula:

📌 r = \frac{a + b - c}{2}

📌 where $ a $ and $ b $ are the legs and $ c $ is the hypotenuse. Substituting:

📌 r = \frac{3k + 4k - 5k}{2} = \frac{2k}{2} = k

📌 So $ k = r $. Now compute the area of the triangle:

📌 \text{Area} = \frac{1}{2} \cdot 3k \cdot 4k = 6k^2 = 6r^2

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