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perpendicularity wanted, starting with tangent circles

Source: Norwegian Mathematical Olympiad 1995 - Abel Competition p2a

February 11, 2020
tangent circlesgeometrycirclesperpendicular

Problem Statement

Two circles k1,k2k_1,k_2 touch each other at PP, and touch a line ℓ\ell at AA and BB respectively. Line APAP meets k2k_2 at CC. Prove that BCBC is perpendicular to ℓ\ell.
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