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Use the Sine Rule to find the radius of the circumcircle.

Mathematics

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Step 1: Use the Sine Rule to find the radius of the circumcircle.
The Sine Rule states that for any triangle with sides a,b,ca, b, c and opposite angles A,B,CA, B, C, respectively, and circumradius RR:

asin⁡A=bsin⁡B=csin⁡C=2R\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R

In triangle RSQ, we are given:
Side QR=12 cmQR = 12 \text{ cm}
Angle ∠RSQ=50∘\angle RSQ = 50^\circ (This angle is opposite to side QRQR)

Step 2: Substitute the given values into the Sine Rule formula.

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