CMO 1976 Problem 4

Let $AB$ be a diameter of a circle, $C$ be any fixed point between $A$ and $B$ on this diameter, and $Q$ be a variable point on the circumference of the circle. Let $P$ be the point on the line determined by $Q$ and $C$ for which $\frac{AC}{CB}=\frac{QC}{CP}$ . Describe, with proof, the locus of the point $P$ .