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ASU 022 All Russian MO 1962 10.1 perpendicularity in isosceles

Source:

June 17, 2019
geometryisoscelesperpendicular

Problem Statement

The MM point is the midpoint of the base [AC][AC] of an isosceles triangle ABCABC. [MH][MH] is orthogonal to [BC][BC] side. Point PP is the midpoint of the segment [MH][MH]. Prove that [AH][AH] is orthogonal to [BP][BP].
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