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if <C_1MA_1=<ABC then C_1 K=A_1L (Caucasus 2015 for the 10th grade)

Source: I Caucasus 2015 10.5

September 6, 2018
geometryaltitudesmidpointsequal anglesequal segments

Problem Statement

Let AA1AA_1 and CC1CC_1 be the altitudes of the acute-angled triangle ABCABC. Let K,LK,L and MM be the midpoints of the sides AB,BCAB,BC and CACA respectively. Prove that if ∠C1MA1=∠ABC\angle C_1MA_1 =\angle ABC, then C1K=A1LC_1 K = A_1L.
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