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ME = BC wanted, AE = MD, AN = AM, <BAC = 135^o, circumcircle

Source: 2017 Thailand October Camp 3.2

October 15, 2020
geometryequal segmentscircumcircle

Problem Statement

In triangle △ABC\vartriangle ABC, ∠BAC=135o\angle BAC = 135^o. MM is the midpoint of BCBC, and N≠MN \ne M is on BCBC such that AN=AMAN = AM. The line AMAM meets the circumcircle of △ABC\vartriangle ABC at DD. Point EE is chosen on segment ANAN such that AE=MDAE = MD. Show that ME=BCME = BC.
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