Question 192
Let $ABC$ be a scalene triangle and let $I$ be its incenter. Consider the circles $\gamma$, $\delta$, of diameters $IB$, respectively $IC$. The circles $\gamma'$, $\delta'$ are the mirror images of $\gamma$, $\delta$ in $IC$, respectively $IB$. Prove that the circumcenter of the triangle $ABC$ lies on the line joining the common points of the circles $\gamma'$ and $\delta'$.
Cosmin Pohoăță
Cosmin Pohoăță