Question 106
A circle $k_{1}$ lies within a second circle $k_{2}$ and touches it at the point $A$. A straight line through $A$ cuts $k_{1}$ again into $B$ and $k_{2}$ into $C$. The tangent to $k_{1}$ through $B$ intersects $k_{2}$ at the points $D$ and $E$. The tangents to $k_{1}$ through $C$ touch $k_{1}$ at the points $F$ and $G$. Prove that $D, E, F$ and $G$ lie on a circle.
