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Points on a triangle

Source: Indonesia Mathematics Olympiad 2007 Day 1 Problem 1

June 2, 2008
geometryperpendicular bisectorgeometry proposed

Problem Statement

Let ABC ABC be a triangle with \angle ABC\equal{}\angle ACB\equal{}70^{\circ}. Let point D D on side BC BC such that AD AD is the altitude, point E E on side AB AB such that \angle ACE\equal{}10^{\circ}, and point F F is the intersection of AD AD and CE CE. Prove that CF\equal{}BC.
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