Let \gamma and \Gamma be two circles such that \gamma is internally tangent to \Gamma at a point X. Let P be a point on the common tangent of \gamma and \Gamma and Y be the point on \gamma other than X such that P Y is tangent to \gamma at Y. Let P Y intersect \Gamma at A and B, such that A is in between P and B and let the tangents to \Gamma at A and B intersect at C. C X intersects \Gamma again at Z and Z Y intersects \Gamma again at Q. If A Q=6, A B=10 and \frac{A X}{X B}=\frac{1}{4}. The length of Q Z=\frac{p}{q} \sqrt{r}, where p and q are coprime positive integers, and r is square free positive integer. Find p+q+r.