Problem 8.
A circle of radius r is inscribed inside a triangle whose sides are 13, 14, and 15 units long. Find the radius of the circle.

Solution:

First, find the area of the triangle using the semiperimeter s is given as follows:

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The area of the triangle A given its 3 sides is:


Now draw a line from each vertex of the triangle to the center of the circle.
This divides the triangle into 3 smaller triangles whose altitudes are r and whose
bases are 13, 14, and 15. The area of the large triangle 84, is the sum of the areas of the 3 smaller triangles. Therefore,