Question 67
Points $M,X,Y$ lie on the sides $AB,AC,BC$, respectively, of triangle $ABC$, with $AX=MX$ and $BY=MY$. Let $K,L$ be the midpoints of $AY,BX$, and $O$ the circumcenter of $ABC$. Let $O_1,O_2$ be the reflections of $O$ in $K,L$, respectively. Prove that $X,Y,O_1,O_2$ are concyclic.
