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Home » So, number of favorable selections: - DNSFLEX

So, number of favorable selections: - DNSFLEX

📅 March 12, 2026 👤 scraface

Mar 12, 2026

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📌 Solution: The area $A_{\text{circle}}$ of the inscribed circle is:

📌 The area $A_{\text{triangle}}$ of a right triangle with legs $a$ and $b$ and hypotenuse $t$ is:

📌 A_{\text{triangle}} = \frac{1}{2}ab

📌 The radius $r$ of the incircle of a right triangle is given by:

📌 r = \frac{a + b - t}{2}

📌 \frac{\pi r^2}{\frac{1}{2}ab} = \frac{2\pi r^2}{ab}

📌 Substituting $r = \frac{a + b - t}{2}$:

📌 \frac{2\pi \left(\frac{a + b - t}{2}\right)^2}{ab} = \frac{2\pi \cdot \frac{(a + b - t)^2}{4}}{ab} = \frac{\pi (a + b - t)^2}{2ab}

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