A bend in a road is formed from two concentric arcs with inside radius and outside radius , each of a third of a circle with the same centre. The road is then formed of tangents to the arcs. A cyclist cuts the corner by following an arc of radius which is tangent to the outside of the road at its ends and tangent to the inside of the road in the middle. Prove that for some number to be found.
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Maclaurin Mathematical Olympiad (2024)
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