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Prove that DL=DM

Source: IMO LongList 1982 - P30

September 10, 2010
trigonometrygeometryTrianglemidpointIMO ShortlistIMO Longlist

Problem Statement

Let ABCABC be a triangle, and let PP be a point inside it such that ∠PAC=∠PBC\angle PAC = \angle PBC. The perpendiculars from PP to BCBC and CACA meet these lines at LL and MM, respectively, and DD is the midpoint of ABAB. Prove that DL=DM.DL = DM.
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