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Easy geo

Source: Mongolian Mathematical Olympiad P2

January 30, 2024
geometry

Problem Statement

In an acute triangle ABCABC the points D,ED, E are the feet of the altitudes through B,CB, C respectively. Let LL be the point on segment BDBD such that AD=DLAD=DL. Similarly, let KK be the point on segment CECE such that AE=EKAE=EK. Let MM be the midpoint of KLKL. The circumcircle of ABCABC intersect the lines ALAL and AKAK for a second time at T,ST, S respectively. Prove that the lines BS,CT,AMBS, CT, AM are concurrent.
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