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angle bisestor of <APC passes throug D, ABCD parallelogram, AM=CN,

Source: 2004 Estonia National Olympiad Final Round grade 10 p2

March 25, 2020
geometryangle bisectorparallelogramequal segments

Problem Statement

On side, BC,ABBC, AB of a parallelogram ABCDABCD lie points M,NM,N respectively such that ∣AM∣=∣CN∣|AM| =|CN|. Let PP be the intersection of AMAM and CNCN. Prove that the angle bisector of ∠APC\angle APC passes through DD.
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