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

February 22, 2026

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

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h_a = \frac{2A}{a} = \frac{2 \times 84}{13} = \frac{168}{13} \approx 12.92
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 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:

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