Question 79
Let $ABC$ be an acute, scalene triangle with orthocenter $H$. Let $l_a$ be the line through the reflection of $B$ with respect to $CH$ and the reflection of $C$ with respect to $BH$. Lines $l_b$ and $l_c$ are defined similarly. Suppose lines $l_a, l_b$, and $l_c$ determine a triangle. Prove that the orthocenter and circumcenter of this triangle are colinear with $H$.