Question 169
Given an acute triangle $ABC$ with $O$ as its circumcenter. Line $AO$ and side $BC$ meet at $D$. Points $E$ and $F$ are on sides $AB$ and $AC$ respectively, such that points $A$, $E$, $D$ and $F$ are on a circle. Prove that the length of the projection of line segment $EF$ on side $BC$ does not depend on the positions of $E$ and $F$. (posed by Xiong Bin)