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Tangents from two disjoint circles: show that AB=MN

Source: Isi (BS) 2008 #4

May 4, 2012
geometry unsolvedgeometry

Problem Statement

Suppose PP and QQ are the centres of two disjoint circles C1C_1 and C2C_2 respectively, such that PP lies outside C2C_2 and QQ lies outside C1C_1. Two tangents are drawn from the point PP to the circle C2C_2, which intersect the circle C1C_1 at point AA and BB. Similarly, two tangents are drawn from the point QQ to the circle C1C_1, which intersect the circle C2C_2 at points MM and NN. Show that AB=MNAB=MN
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