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equal segments, circles, tangents (1999 Argentina OMA L2 p2)

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June 16, 2020
geometrysegmentscirclesTangents

Problem Statement

Let C1C_1 and C2C_2 be the outer circumferences of centers O1O_1 and O2O_2, respectively. The two tangents to the circumference C2C_2 are drawn by O1O_1, intersecting C1C_1 at PP and P′P'. The two tangents to the circumference C1C_1 are drawn by O2O_2, intersecting C2C_2 at QQ and Q′Q'. Prove that the segment PP′PP' is equal to the segment QQ′QQ'.
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