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UKMT Pink Kangaroo, 2026

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Two perpendicular chords are drawn in a circle with radius 12 cm, dividing the circle into four regions, as labelled in the diagram. One chord lies 3 cm from the centre, and the other lies 4 cm from the centre. The sum of the areas of regions $J$ and $M$ is $X$ cm $^2$ larger than the sum of the areas of regions $K$ and $L$ . What is the value of $X$ ?

(A) $9$ (B) $16$ (C) $36$ (D) $48$ (E) $60$

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