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BMO Shortlist 2021 G6

Source: BMO Shortlist 2021

May 8, 2022
Balkanshortlist2021geometrycollinearityBMO

Problem Statement

Let ABCABC be an acute triangle such that AB<ACAB < AC. Let ω\omega be the circumcircle of ABCABC and assume that the tangent to ω\omega at AA intersects the line BCBC at DD. Let Ω\Omega be the circle with center DD and radius ADAD. Denote by EE the second intersection point of ω\omega and Ω\Omega. Let MM be the midpoint of BCBC. If the line BEBE meets Ω\Omega again at XX, and the line CXCX meets Ω\Omega for the second time at YY, show that A,YA, Y, and MM are collinear.
Proposed by Nikola Velov, North Macedonia
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