IMO 1992 LL USA78

Origin: USA

Problem

Let Fn be the nth Fibonacci number, defined by F1 = F2 = 1 and Fn = Fn−1 + Fn−2 for n > 2. Let A0, A1, A2, . . . be a sequence of points on a circle of radius 1 such that the minor arc from Ak−1 to Ak runs clockwise and such that µ(Ak−1Ak) = 4F2k+1 F 2 2k+1 + 1 for k \geq1, where µ(XY ) denotes the radian measure of the arc XY in the clockwise direction. What is the limit of the radian measure of arc A0An as n approaches infinity?