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.
Sreejato Bhattacharya by Sreejato Bhattacharya
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