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📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Final answer: $ \boxed{1} $

📌 Question: The hypotenuse of a right triangle is $ h $, and the radius of the inscribed circle is $ r $. What is the ratio of the area of the circle to the area of the triangle?

📌 The area of a right triangle with inradius $ r $ and hypotenuse $ h $ is given by:

📌 A_{\text{triangle}} = r \cdot \frac{a + b + h}{2}

📌 But in a right triangle, the inradius is related to the sides $ a, b, h $ by:

📌 r = \frac{a + b - h}{2}

📌 Also, the area of the triangle is:

📌 However, using the inradius formula, we can express the triangle’s area as:

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