Two circles, the sum of whose radii is \(a\), are placed in the same place with their centers at a distance \(2a\), and an endless string, quite stretched, partly surrounds the circles and crosses itself between them. Prove that the length of the string is \((\frac{4}{3}\pi + 2\sqrt{3})a\).
A Treatise on Plane Trigonometry, Ernest Hobson, 1891