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Circular Fun (Posted on 2005-07-28) Difficulty: 2 of 5
When you draw three circles of radius r such that all three are externally tangent, what is the area of the shape in the center in terms of r?

See The Solution Submitted by Justin    
Rating: 3.2857 (7 votes)

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Solution re: solution..... :) | Comment 9 of 18 |
(In reply to solution..... :) by josh_79_97)


When 3 circles of equal radius are externally tangent to one another, an equallateral triangle with sides of 2R is formed by drawing lines through their center points. Thus: area of the triangle = (2R)(2R cosR)(1/2).

Each corner of the triangle is digging into 1/6 of each circle. Thus: the area of each slice of pie = R /6.

Sence there are 3 "slices of pie" inside the traingle, then the remainder or, the shape in the center, would be:

(2R)(2R cosR)(1/2) - ( R /6)(3)

  Posted by josh_79_97 on 2005-08-01 22:20:37
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