Question 15
In triangle $ABC$ with $CA = CB$, point $E$ lies on the circumcircle of $ABC$ such that $\angle ECB = 90^\circ$. The line through $E$ parallel to $CB$ intersects $CA$ in $F$ and $AB$ in $G$. Prove that the centre of the circumcircle of triangle $EGB$ lies on the circumcircle of triangle $ECF$.