CMO 2015 Problem 2

Let $A, B, D, E, F, C$ be six points lie on a circle (in order) satisfy $AB=AC$ . Let $P=AD \cap BE, R=AF \cap CE, Q=BF \cap CD, S=AD \cap BF, T=AF \cap CD$ . Let $K$ be a point lie on $ST$ satisfy $\angle QKS=\angle ECA$ .

Prove that $\frac{SK}{KT}=\frac{PQ}{QR}$