Question 17
Let $\triangle ABC$ be an acute triangle with $|AB| \gt |AC|$. Let $D$ be a point on the side $AB$, such that the angles $\angle ACD$ and $\angle CBD$ are equal. Let $E$ denote the midpoint of $BD$, and let $S$ be the circumcentre of the triangle $BCD$. Prove that the points $A, E, S$ and $C$ lie on the same circle.