Question 46
Consider the acute triangle $ABC$ with circumcenter $O$ and orthocenter $H$. Outside the triangle, construct the segments $CF \perp BC$ with $CF = \frac{AC}{2}$ and $CG \perp AC$ with $CG = \frac{BC}{2}$. Let $X$ be the point of intersection $OC \cap FG$. Prove that:
$$
\overrightarrow{OX} = \frac{\overrightarrow{OH} - \overrightarrow{OA} + \overrightarrow{BF} + \overrightarrow{AG}}{2}.
$$
Mihaela Berindeanu
$$
\overrightarrow{OX} = \frac{\overrightarrow{OH} - \overrightarrow{OA} + \overrightarrow{BF} + \overrightarrow{AG}}{2}.
$$
Mihaela Berindeanu