Given a circle with center O and radii OP = OQ = OR = 5 cm, and chords PQ = 4 cm and QR = 9 cm, calculate the angle PQR.

Step 1: Identify the given information from the problem and the diagram.
The circle has center O.
The radii are $OP = OQ = OR = 5$ cm.
The lengths of the chords are $PQ = 4$ cm and $QR = 9$ cm.
We need to calculate $\angle PQR$.

Step 2: Calculate $\angle POQ$ using the Cosine Rule in $\triangle POQ$.
The sides of $\triangle POQ$ are $OP=5$ cm, $OQ=5$ cm, and $PQ=4$ cm.
The Cosine Rule states $c^2 = a^2 + b^2 - 2ab \cos C$.

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