Question 36
Let $I$ be the incenter and $H$ the orthocenter of triangle $ABC$. A point $K$ in the plane satisfies
$$
AH + AK = BH + BK = CH + CK.
$$
Prove that $H$, $I$, $K$ are collinear.
$$
AH + AK = BH + BK = CH + CK.
$$
Prove that $H$, $I$, $K$ are collinear.