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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 where \( z = \sqrt{a^2 + b^2} \). Also, the area can express in terms of the inradius:

📌 A = c \cdot s,

📌 where \( s = \frac{a + b + z}{2} \) is the semi-perimeter.

📌 A_{\text{circle}} = \pi c^2.

📌 Thus, the ratio \( R \) of the area of the circle to the area of the triangle is:

📌 R = \frac{\pi c^2}{A} = \frac{\pi c^2}{c \cdot s} = \frac{\pi c}{s}.

📌 For a right triangle, it is known that \( r = \frac{a + b - c}{2} \), and also \( A = r s \), so the ratio simplifies to:

📌 R = \frac{\pi c}{s}.

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