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In the figure below, O is the center of the circle. Find the value of ACB.

Mathematics

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Step 1: Use the cosine rule to find ∠Q\angle Q.

cos⁡Q=PQ2+QR2−PR22⋅PQ⋅QR\cos Q = \frac{PQ^{2} + QR^{2} - PR^{2}}{2 \cdot PQ \cdot QR}

Step 2: Substitute the side lengths PQ=8.3PQ = 8.3 cm, QR=9.2QR = 9.2 cm, PR=7.6PR = 7.6 cm.

PQ2=8.32=68.89 cm2PQ^{2} = 8.3^{2} = 68.89\, \mathrm{cm}^{2}
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