+++++++++ +++ +++ +S ++ + \ + +  \ + +  \ + +  \ _Q +  \ O _ /+ +  \ _ / + +  \ _ / + AXCYB +  _ \ / + ++ _ \ / ++ P+++ \ /++ ++++++++R 
In circle O, a chord AB is drawn, with midpoint C. Through C, two more
chords are drawn, PQ and RS. Connecting the endpoints, PS passes through
AC at point X, and QR passes through BC at point Y. Show that CX = CY.
First try showing:

Source: The rec.puzzles newsgroup long ago, though I can't find it in the rec.puzzles archive.