Two circles whose radii have sum are placed in the same plane with their centres apart

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Two circles whose radii have sum aa are placed in the same plane with their centres 2a2a apart. An endless string is fully stretched so as partly to surround the circles and to cross between them. Prove that the length of the string is (4π3+23)a\left(\frac{4\pi}{3}+2\sqrt3\right)a.

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