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Equal areas condition

Source: 2008 Bulgarian Autumn Math Competition, Problem 10.2

March 18, 2022
geometrymidpointarea of a triangle

Problem Statement

Let △ABC\triangle ABC have MM as the midpoint of BCBC and let PP and QQ be the feet of the altitudes from MM to ABAB and ACAC respectively. Find ∠BAC\angle BAC if [MPQ]=14[ABC][MPQ]=\frac{1}{4}[ABC] and PP and QQ lie on the segments ABAB and ACAC.
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