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Bisection in internally tangent circles

Source: XVII Sharygin Correspondence Round, P16

March 2, 2021
circlegeometry

Problem Statement

Let circles Ω\Omega and ω\omega touch internally at point AA. A chord BCBC of Ω\Omega touches ω\omega at point KK. Let OO be the center of ω\omega. Prove that the circle BOCBOC bisects segment AKAK.
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