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colinear points

Source: Swiss IMO TST 2016. Problem 10

July 27, 2017
aligned pointsgeometry

Problem Statement

Let ABCABC be a non-rectangle triangle with MM the middle of BCBC. Let DD be a point on the line ABAB such that CA=CDCA=CD and let EE be a point on the line BCBC such that EB=EDEB=ED. The parallel to EDED passing through AA intersects the line MDMD at the point II and the line AMAM intersects the line EDED at the point JJ. Show that the points C,IC, I and JJ are aligned.
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