Question 66
An isosceles triangle $ABC$ is inscribed in a circle with $\angle ACB = 90^\circ$ and $EF$ is a chord of the circle such that neither $E$ nor $F$ coincide with $C$. Lines $CE$ and $CF$ meet $AB$ at $D$ and $G$ respectively. Prove $|CE| \cdot |DG| = |EF| \cdot |CG|$.