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Question:** A triangle has sides of lengths 13 cm 14 cm and 15 cm. Find the radius of the inscribed circle.

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Solution:

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To find the radius \( r \) of the inscribed circle (inradius) we use the formula:

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r = \frac{A}{s}

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where \( A \) is the area of the triangle and \( s \) is the semi-perimeter.

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First compute the semi-perimeter:

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s = \frac{13 + 14 + 15}{2} = \frac{42}{2} = 21 \ \text{cm}

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