Question 73
Two circles $k_{1}$ and $k_{2}$ intersect at $A$ and $B$. Let $r$ be a line through $B$ that meets $k_{1}$ at $C$ and $k_{2}$ at $D$, such that $B$ lies between $C$ and $D$. Let $s$ be the line parallel to $AD$ that touches $k_{1}$ at $E$ and has the smallest possible distance from $AD$. The line $AE$ meets $k_{2}$ at $F$. Let $t$ be the tangent to $k_{2}$ at $F$. Prove that:
(a) The line $t$ is parallel to $AC$.
(b) The lines $r$, $s$ and $t$ meet in a single point.
(a) The line $t$ is parallel to $AC$.
(b) The lines $r$, $s$ and $t$ meet in a single point.