Consider three circles $C_1,C_2\text{and}{C}_3$ such that $C_2$ is the director circle of $C_1,\text{and}{C}_3$ is the director circlé of $C_2$. Tangents to $C_1$, from any point on $C_3$ intersect $C_2$, at $P^2\text{and}Q$. Find the angle between the tangents to $C_2^2$ at P and Q. Also identify the locus of the point of intersec- tion of tangents at $P\text{and}Q$.

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