[  Radii of the inscribed, circumscribed, and exscribed circles (other). [ Area of a triangle (using the semiperimeter and the radius of the inscribed or exscribed circle).

A circle is inscribed in a right triangle. One of the legs is divided by the point of tangency into segments of 6 and 10, measured from the vertex of the right angle. Find the area of the triangle.

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Given that the radius of the inscribed circle is 6, and one of the legs is 16. Let the second leg be $b$. Then the semiperimeter $p=b+16-6=b+10$. By calculating the area $S$ of the triangle in two ways, we get $8b = S = 6(b+10)$, from which $b=30$.

## Answer

240.