You are given a circle of radius 1 unit and two circles of radius a and b which touch each other and also touch the unit circle. Prove that you can always draw a 'flower' with six petals with the unit circle in the middle, and six circles around it having radii
a, b, b/a, 1/a, 1/b and a/b
such that each outer circle touches the unit circle and the two circles on either side of it.
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