MEMO 2012 pojedinačno problem 3

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June 23, 2013
In a given trapezium ABCD with AB parallel to CD and AB > CD, the line BD bisects the angle \angle ADC. The line through C parallel to AD meets the segments BD and AB in E and F, respectively. Let O be the circumcenter of the triangle BEF. Suppose that \angle ACO = 60^{\circ}. Prove the equality
CF = AF + FO .
Source: Srednjoeuropska matematička olimpijada 2012, pojedinačno natjecanje, problem 3