Two Circles in a Box
Given the two circles as in the picture. They are tangent to each other, and the bottom side, and their side of the rectangle. The bottom has length 20. Find .
Give your answer to 2 decimal places.
The answer is 3.43.
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1 solution
the line connecting centers is 3R. Through center of small circle draw horizontal line. Through center of large circle draw vertical line.
This forms a right triangle with vertical leg = R, hypotenuse = 3R. Using Pythagorean's Theorem, the horizontal leg is R*sqrt(8).
Length of rectangle = 3R + R*sqrt(8) = 20 which yields R = 3.43