MathDB

In right triangle

ABC

with right angle

C

CA=30

and

CB=16

. Its legs

\overline{CA}

and

\overline{CB}

are extended beyond

A

and

B

. Points

O_{1}

and

O_{2}

lie in the exterior of the triangle and are the centers of two circles with equal radii. The circle with center

O_{1}

is tangent to the hypotenuse and to the extension of leg CA, the circle with center

O_{2}

is tangent to the hypotenuse and to the extension of leg CB, and the circles are externally tangent to each other. The length of the radius of either circle can be expressed as

p/q

, where

p

and

q

are relatively prime positive integers. Find

p+q

Problem Statement