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contruct a point with equal angles related to bases of altitudes

Source: 2011 Sharygin Geometry Olympiad Correspondence Round P12

April 4, 2019
geometryequal anglesconstructionaltitudes

Problem Statement

Let APAP and BQBQ be the altitudes of acute-angled triangle ABCABC. Using a compass and a ruler, construct a point MM on side ABAB such that ∠AQM=∠BPM\angle AQM = \angle BPM.
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