Question 109
Let $ABC$ be an acute-angled triangle with $AC \lt BC$; let $M$ be the midpoint of $AB$. Let $CC'$ be a diameter in the circumcircle $\Omega$ of the triangle $ABC$. The line $CM$ meets the lines $AC'$ and $BC'$ at $K$ and $L$, respectively. Denote by $\Delta$ the triangle formed by the line through $K$ perpendicular to $AC'$, the line through $L$ perpendicular to $BC'$, and the line $AB$. Prove that the circumcircle of $\Delta$ is tangent to $\Omega$.
(M. Kungozhin)
(M. Kungozhin)