# Two Perpindicular Curves

Geometry Level 3

In circle $$\Gamma$$, 2 chords $$AB$$ and $$CD$$ are perpendicular at $$E$$. If $$AE = 2 , EB = 5$$ and $$EC = 3$$, then the radius of $$\Gamma$$ can be expressed as $$\frac { \sqrt{a} } {b}$$, where $$a$$ is an integer that is not divisible by the square of any prime and $$b$$ is a positive integer. What is the value of $$a + b$$?

Note: $$a$$ and $$b$$ need not be coprime.

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