VMO 2000 Problem 2
C and C' are circles centers O and O' respectively. X and X' are points on C and C' respectively such that the lines OX and O'X' intersect. M and M' are variable points on C and C' respectively, such that ∠XOM = ∠X'O'M' (both measured clockwise). Find the locus of the midpoint of MM'. Let OM and O'M' meet at Q. Show that the circumcircle of QMM' passes through a fixed point.
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