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