Inspired by My Best Friend - 2

Geometry Level 5

Let '\(P\)' and '\(Q\)' be two conjugate points with respect to the circle of radius \(20\) units. Let the lengths of the tangents from \(P\) and \(Q\) onto circle be \(20\), \(24\) respectively.

If the length of the segment \(PQ\) can be expressed in the form of \(a\sqrt{b}\); where \(a\), \(b\) are positive integers and \(b\) is square free. Find \(a+b\).

Details and Assumptions:

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