Two Touching Circles

A circle with radius \(r\) is tangent internally to a larger circle with centre \(A\) and radius \(3\) at a point \(B\). Points \(P\) and \(Q\) on the larger circle are such that \(\overline{AP}\) and \(\overline{AQ}\) are tangent to the smaller circle. If the area of \(\triangle APQ\) is , the sum of all possible values of r can be expressed as \(a\sqrt[b]{c} + d\), where a, b, c, and d are integers. Find the smallest value of \(a+b+c+d\)