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collinearity of intersections of diameters of 3 chords

Source: Mexican Mathematical Olympiad 1993 OMM P5

July 29, 2018
geometrycollinearChords

Problem Statement

OA,OB,OCOA, OB, OC are three chords of a circle. The circles with diameters OA,OBOA, OB meet again at ZZ, the circles with diameters OB,OCOB, OC meet again at XX, and the circles with diameters OC,OAOC, OA meet again at YY. Show that X,Y,ZX, Y, Z are collinear.
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