Question 79
Inside the circle $\Gamma$ are three circles $\gamma_{1}$, $\gamma_{2}$ and $\gamma_{3}$, and tangents at $\Gamma$ respectively In $A$, $B$ and $C$, all separate. The circles $\gamma_{2}$ and $\gamma_{3}$ have a common point $K$ that belongs to $[BC]$, the circles $\gamma_{3}$ and $\gamma_{1}$ have a common point $L$ that belongs to $[CA]$, and the circles $\gamma_{1}$ and $\gamma_{2}$ have a common point $M$ which belongs to $[AB]$. Prove that the center of $\Gamma$ belongs to $\gamma_{1}$, $\gamma_{2}$ and $\gamma_{3}$.