Question 86
The circles $K_1$ and $K_2$ with the centres $O_1$ and $O_2$ intersect at the points $A$ and $B$, so that $\angle O_1AO_2 \gt \frac{\pi}{2}$. The line $O_1B$ intersects the circle $K_2$ again at $C$, the line $O_2B$ intersects the circle $K_1$ again at $D$. The line through the point $B$ parallel to the line $CD$ intersects the circles at $E$ and $F$. Prove that $|EF| = |AC| + |AD|$.
