Point in the interior
Source: 2019 Second Round - Poland
July 8, 2019
geometrylengthsangles
Problem Statement
Let be a point lying in the interior of the acute triangle such that
\begin{align*}
\sphericalangle BAX = 2\sphericalangle XBA \ \ \ \ \hbox{and} \ \ \ \ \sphericalangle XAC = 2\sphericalangle ACX.
\end{align*}
Denote by the midpoint of the arc of the circumcircle containing . Prove that .