Question 17
Let $ABC$ be a triangle inscribed in a circle $(O)$. Let $D$ be a point on the arc $BC$ not containing $A$. Suppose that the tangent of $(O)$ at $D$ meets $BC$ at $E$. The circumcircle of $ODE$ meets $AD$ at second point $F$ (different to $D$). The line $EF$ meets $AB$ at $M$, the line $DM$ meet $(O)$ at the second point $K$ (different to $D$).
Prove that $K,F,C$ are collinear.
Prove that $K,F,C$ are collinear.