Question 118
Let $[AB]$ be a chord of a circle $(c)$ centered at $O$, and let $K$ be a point on the segment $(AB)$ such that $AK \lt BK$. Two circles through $K$, internally tangent to $(c)$ at $A$ and $B$, respectively, meet again at $L$. Let $P$ be one of the points of intersection of the line $KL$ and the circle $(c)$, and let the lines $AB$ and $LO$ meet at $M$. Prove that the line $MP$ is tangent to the circle $(c)$.
