Consider two concentric circles C1: x^2+y^2=1, C2: x^2+y^2=4. Tangent are drawn to C1 from any point P on C2. These tangents again meet circle C2 at A & B. Prove that the line joining A & B will touch C1. Further, find the locus of the point of intersection of tangents drawn to C2 at A & B.

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Consider two concentric circles C1: x^2+y^2=1, C2: x^2+y^2=4. Tangent are drawn to C1 from any point P on C2. These tangents again meet circle C2 at A & B. Prove that the line joining A & B will touch C1. Further, find the locus of the point of intersection of tangents drawn to C2 at A & B.

Consider two concentric circles C1: x^2+y^2=1, C2: x^2+y^2=4. Tangent are drawn to C1 from any point P on C2. These tangents again meet circle C2 at A & B. Prove that the line joining A & B will touch C1. Further, find the locus of the point of intersection of tangents drawn to C2 at A & B.

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