SOLUTION: A circle is inscribed into a right triangle. The point of tangency divides the hypotenuse in two segments with lengths 2 and 3. Find the radius of the circle

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Question 1155987: A circle is inscribed into a right triangle. The point of tangency divides the hypotenuse in two segments with lengths 2 and 3. Find the radius of the circle
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let the triangle be ABC, with right angle at C.

Let P, Q, and R be the points of tangency of the circle with sides AB, BC, and CA, respectively.

We are given that AP=2 and PB=3.

Two tangents from an external point to a circle are congruent, so RC=2 and QB=3.

If r is the radius of the circle, then AC = 2+r and BC = 3+r.

Then in triangle ABC,

%282%2Br%29%5E2%2B%283%2Br%29%5E2+=+5%5E2

That equation is easily solved to find the radius.