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Triangle is Isosceles

Source: 2010 IrMO Paper 1 Problem 2

January 30, 2018
geometry

Problem Statement

Let ABCABC be a triangle and let PP denote the midpoint of the side BCBC. Suppose that there exist two points MM and NN interior to the side ABAB and ACAC respectively, such that ∣AD∣=∣DM∣=2∣DN∣,|AD|=|DM|=2|DN|, where DD is the intersection point of the lines MNMN and APAP. Show that ∣AC∣=∣BC∣|AC|=|BC|.
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