perplexus.info :: Geometry : Complicated Tangency

Complicated Tangency (Posted on 2018-09-01)

Nine circles of radius 0.5 are externally tangent to a circle of radius 1 and also are tangent to one another.

Find the distance between the centers of the first and the last of the smaller circles.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution in one line on a calculator

| Comment 1 of 2

sin((360-8*2*arcsin(0.5/1.5))/2)*1.5*2

Which simplifies to

3sin(8arcsin(1/3)) = 1904sqrt(2)/2187

or about 1.231213

Posted by Jer on 2018-09-01 13:59:30

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