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Estonian Math Competitions 2005/2006

Source: Seniors Problem 8

July 30, 2008
geometry unsolvedgeometry

Problem Statement

Four points A,B,C,D A, B, C, D are chosen on a circle in such a way that arcs AB,BC, AB, BC, and CD CD are of the same length and the arcDA arc DA is longer than these three. Line AD AD and the line tangent to the circle at B B intersect at E E. Let F F be the other endpoint of the diameter starting at C C of the circle. Prove that triangle DEF DEF is equilateral.
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