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Question: In a right triangle, the hypotenuse is $ z $, and the inradius is $ c $. Express the ratio of the area of the inscribed circle to the triangles area in terms of $ z $ and $ c $.
Question: A historical surveyor measured a triangular plot with sides 15, 20, 25 meters. Determine the length of the altitude from the right angle to the hypotenuse.
The other two altitudes correspond to the equal sides as bases. We compute the area of the triangle first:

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