Question 12
Let acute triangle $ABC$ be isosceles at $A$ and inscribed in $(O)$. Choose $D$ on minor arc $BC$ with $DB\lt DC$. Lines through $B,C$ parallel to $AD$ meet the circle again at $E,F$. Choose $K$ on minor arc $AE$, distinct from $A,E$. Let $M=KE\cap AC$ and $N=KF\cap AB$. Prove that $MN,KD,BC$ are concurrent.