Question 17
Circle $\left(O\right)$ has diameter $AB$ and $D$ is the midpoint of arc $AB$. $M$ lies on $AB$ extended outside the circle; $MD$ meets the circle again at $C$. Circle $\left(I\right)$ through $D , C$ is tangent to $AB$ at $K$; $DK$ meets $\left(O\right)$ again at $E$. Prove $ME$ is tangent to $\left(O\right)$.