The Internal Angle Bisector

Geometry Level 3

In $\triangle ABC$ , $\angle ABC = 30°.$ Points $P$ and $Q$ are chosen on $\overline{AC}$ such that $AP+BC= AB+CQ$ . The internal angle bisector of $\angle ABC$ intersects $\overline{AC}$ at $R$ .

Given that $R$ is the midpoint of $PQ$ , find $\angle BAC$ (in degrees).

The Internal Angle Bisector

This problem has been adapted from the Proofathon Geometry contest, and was posed by Shivang Jindal.