Question 133
Let $ABC$ be an acute triangle with $m(\angle BAC)=60^{\circ}$ and $BC=a$. Let $M$ be the midpoint of side $BC$, and let $[BB_{1}]$ and $[CC_{1}]$ be two altitudes of the triangle. Compute the sum of the distances from the orthocenter of triangle $ABC$ to the sides of triangle $MB_{1}C_{1}$.