Question 3
As seen in Fig. 1.1, $AB$ is a chord of circle $\omega$, $P$ is a point on arc $AB$, and $E, F$ are 2 points on $AB$ satisfying $AE = EF = FB$. Connect $PE, PF$ and extend them to intersect with $\omega$ at $C, D$, respectively. Prove
$$
EF \cdot CD = AC \cdot BD.
$$
Fig. 1.1
$$
EF \cdot CD = AC \cdot BD.
$$
Fig. 1.1