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Middle European Mathematical Olympiad 2012 - Individuals I-3

Source: Middle European Mathematical Olympiad 2012 - Individuals I-3

September 14, 2012
geometrytrapezoidcircumcirclegeometry proposed

Problem Statement

In a given trapezium ABCD ABCD with AB AB parallel to CD CD and AB>CD AB > CD , the line BD BD bisects the angle ∠ADC \angle ADC . The line through C C parallel to AD AD meets the segments BD BD and AB AB in E E and F F , respectively. Let O O be the circumcenter of the triangle BEF BEF . Suppose that ∠ACO=60∘ \angle ACO = 60^{\circ} . Prove the equality CF=AF+FO. CF = AF + FO .
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