IMO 1978 LL USA42

A, B, C, D, E are points on a circle O with radius equal to r.

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IMO 1978 LL USA42

Origin: USA

Problem

A, B, C, D, E are points on a circle O with radius equal to r. Chords AB and DE are parallel to each other and have length equal to x. Diagonals AC, AD, BE, CE are drawn. If segment XY on O meets AC at X and EC at Y , prove that lines BX and DY meet at Z on the circle.