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UKMT Intermediate Mathematical Challenge, 2026

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

Quarter circle $PRT$ is removed from quarter circle $OQS$ to leave three shaded regions, as shown. $OPRT$ is a square and $OP = 2x$ . What is the total area of the three shaded regions?

(A) $\dfrac{3x^2}{4}$ (B) $x^2$ (C) $2x^2$ (D) $\dfrac{3\pi x^2}{4}$ (E) $\pi x^2$

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