Question 23
Circles $k_{1}$, $k_{2}$, $k_{3}$ intersect as follows: $k_{1} \cap k_{2} = \{A, D\}$, $k_{1} \cap k_{3} = \{B, E\}$, $k_{2} \cap k_{3} = \{C, F\}$. Also, $A B C D E F$ is a non-self-intersecting hexagon. Prove that
$$
A B \cdot C D \cdot E F = B C \cdot D E \cdot F A.
$$
(Hint: first prove that $A D$, $B E$, $C F$ meet at some point $O$.)
$$
A B \cdot C D \cdot E F = B C \cdot D E \cdot F A.
$$
(Hint: first prove that $A D$, $B E$, $C F$ meet at some point $O$.)