Question 79
In a triangle $ABC$ with $|BC| \gt |AC| \gt |AB|$, the perpendicular bisector of $[AC]$ intersects $BC$ at $K$ and the perpendicular bisector of $[BC]$ intersects $AC$ at $L$. If $O$, $O_1$ and $O_2$ are circumcenters of triangles $ABC$, $CKL$ and $OAB$, respectively, show that $OCO_1O_2$ is a parallelogram.