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If largest circle has radius 225 and medium circle has radius 100 in the image, what is the radius of smallest circle?

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Three differently sized circles and a line can be positioned so that they are all mutually tangent to one another, as shown below. If the largest circle has radius 225 and the medium circle has radius 100, what is the radius of the smallest circle?

enter image description here

posted Dec 7, 2017 by anonymous

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2 Answers

0 votes

The answer is:

36

EXPLANATION:

The specialized case for Descartes' Theorem, k4 = k1 + k2 ± 2√(k1k2), where k is defined as the curvature 1/r for each circle.
In this case,
k4 = 1/225 + 1/100 + 2√((1/225)(1/100)) = 1/36, and so r = 36.

answer Dec 27, 2017 by Yasin Hossain Siinan
0 votes

r must be 36

answer Apr 12 by anonymous



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