Fishing for Some Angles

Geometry Level 5

Let \(ABC\) be a triangle with circumcircle \(\omega\). Let the bisector of \(\angle ABC\) meet segment \(AC\) at \(D\) and circle \(\omega\) at \(M \neq B\). The circumcircle of \(\triangle BDC\) meets line \(AB\) at \(E \neq B\), and \(CE\) meets \(\omega\) at \(P \neq C\). The bisector of \(\angle PMC\) meets segment \(AC\) at \(Q \neq C.\) Given that \(PQ = MC,\) determine the degree measure of \(\angle ABC.\)

\(\textit{Proposed by Ray Li} \)

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