4.03: Circle geometry with a tangent

A circle has centre \(C\) and radius \(10\). \(A\) and \(B\) lie on the circle, \(P\) lies beyond \(B\), \(AP\) is tangent, \(BP=x\), \(\angle ACB=\theta\), and the perimeter of triangle \(APC\) is \(38\).