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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