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Consider three circles C1, C2 and C3 suc...

Consider three circles `C_1, C_2 and C_3` such that `C_2` is the director circle of `C_1, and C_3` is the director circle of `C_2`. Tangents to `C_1`, from any point on `C_3` intersect `C_2`, at `P and Q`. Find the angle between the tangents to `C_2` at P and Q. Also identify the locus of the point of intersec- tion of tangents at `P and Q `.

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