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silk road angle chasing , perpendiculars given, equal angles wanted

Source: SRMC 2019 P1

July 16, 2019
geometryAngle Chasingequal anglesaltitudes

Problem Statement

The altitudes of the acute-angled non-isosceles triangle ABC ABC intersect at the point H H . On the segment C1H C_1H , where CC1 CC_1 is the altitude of the triangle, the point K K is marked. Points L L and M M are the feet of perpendiculars from point K K on straight lines AC AC and BC BC , respectively. The lines AM AM and BL BL intersect at N N . Prove that ∠ANK=∠HNL \angle ANK = \angle HNL .
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