Question 85
The points $A$, $M_{1}$, $M_{2}$ and $C$ lie in this order on a line. Let $k_{1}$ be the circle with center $M_{1}$ through $A$ and $k_{2}$ the circle with center $M_{2}$ through $C$. The two circles meet at the points $E$ and $F$. A common tangent to $k_{1}$ and $k_{2}$ touches $k_{1}$ at $B$ and $k_{2}$ at $D$. Show that the lines $AB$, $CD$ and $EF$ meet in one point.