One hundred circles all share the same centre, and they are named C1, C2, C3, and so on up to C100. For each whole number n between 1 and 99 inclusive, a tangent to circle Cn crosses circle Cn+1 at two points that are separated by a distance of 2. Given that C1 has radius 1, find the radius of C100 .
Gabriel T. Prajitura
10
Recursively, R^2_(k + 1) = R^2_k + 1, add for k = 1 to 99, cancel and take the square root.
Funny that if instead you ask for the are in between consecutive circles to be constant you get the same rate of growth and the same answer.
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