Given a triangle \(ABC\), construct two squares \(ABPQ\) and \(ACRS\). Suppose that \(M\) is the midpoint of \(PR\). Join \(MB\) and \(MC\). Find \(\angle BMC\).

**Details and Assumptions**:

\(P\) and \(C\) are on opposite side of \(AB\).

\(R\) and \(B\) are on opposite side of \(AC\).

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