Question 4
Let $ABC$ be a triangle, and let $O$ be the midpoint of $BC$. Draw the tangents $AE,AF$ to the circle $(O)$ with diameter $BC$, where $E,F\in(O)$. The rays $AE,AF$ meet $BC$ at $K,L$, respectively. Let $KF,LE$ meet $(O)$ again at $M,N$, respectively. The circumcircle of triangle $MON$ meets the circles with diameters $AB,AC$ again at $X,Y$, respectively. Prove that $\angle XAB=\angle YAC$.