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the lodge at geneva-on-the-lake - Imagemakers

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 h_b = \frac{2A}{b} = \frac{2 \times 84}{14} = 12

📌 h_c = \frac{2A}{c} = \frac{2 \times 84}{15} = \frac{168}{15} = 11.2

📌 The shortest altitude is \( h_c \), so:

📌 The hypotenuse of a right triangle is \( z \), and the radius of the inscribed circle is \( r \). Express the ratio of the area of the inscribed circle to the area of the triangle in terms of \( r \) and \( z \).

📌 The area \( A \) of the right triangle with hypotenuse \( z \) and legs \( a \) and \( b \) is:

📌 The radius \( r \) of the inscribed circle in a right triangle is given by:

📌 r = \frac{a + b - z}{2}

📌 \text{Area of circle} = \pi r^2

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