MathDB
geometry , collinear points wanted

Source: 12th Dürer Math Competition ,First Round, Category E , P5

August 18, 2020
geometrycollinear pointsparallel

Problem Statement

Let ABCABC be a non-right-angled triangle, with AC≠BCAC\ne BC. Let FF be the midpoint of side BCBC. Let DD be a point on line ABAB satisfyingCA=CDCA=CD,and let EE be a point on line BCBC satisfying EB=EDEB = ED. The line passing through AA and parallel to EDED meets line FDFD at point II. Line AFAF meets line EDED at point JJ. Prove that points CC, II and JJ are collinear.
Back to ProblemsView on AoPS