Weird angle! ... or is is?

Level pending

\(\triangle ABC\) is acute with \(\angle B = 2\angle C\). \(AD \) is the internal bisector of \(\angle A\) such that \( AB = DC\). Find (in degrees) the measure of \(\angle BAC\).

NOTE -I found it in a mathematical contest. I solved it but am looking for a better solution and I'm sure some of you will come up with amazing ones.

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