ITOT 43 Spring 2022 - THPT O - additive practice Question 5

A quadrilateral $ABCD$ is inscribed in a circle $\omega$ with centre $O$. The circumcircle of triangle $AOC$ meets the lines $AB,BC,CD,DA$ for the second time at $M,N,K,L$, respectively. Prove that the lines $MN,KL$ and the tangents to $\omega$ at $A,C$ are all tangent to one circle. (6 points)



Neutral editorial illustration.