IGO 2015 I3

In triangle $ABC$, $M,N,K$ are midpoints of sides $BC,AC,AB$, respectively.Construct two semicircles with diameter $AB,AC$ outside of triangle $ABC$. $MK,MN$ intersect with semicircles in $X,Y$. The tangents to semicircles at $X,Y$ intersect at point $Z$. Prove that $AZ \perp BC$. (Mehdi E'tesami Fard)