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).

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