Given is an acute triangle $ABC$ where $H$ is the intersection of the three altitudes of the triangle. Points $B_1$ and $C_1$ respectively lie on the outer circle of triangle ABC such that $BB_1$ and $CC_1$ are the diameters of the outer circle of triangle $ABC$. Points $D$ and $E$ are the midpoints of sides $AB$ and sides $AC$, respectively. If $DC$ and $BE$ intersect at point $M$, while $B_1D$ and $C_1E$ intersect at point $N$, prove that $BC$ is perpendicular to $MN$.
Is my geometry drawing correct? anyone can help me for this problem solve? Thank you
