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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..... :) | Comment 8 of 18 |

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)(R sin60¨¬)/(sin30¨¬)(1/3).  Each corner of the triangle is digging into 1/6 of each circle. Thus: the area of each slice of pie = (¥ğR©÷)/6.  Sence there are 3 "slices of pie" inside the traingle, then the remainder or, the shape in the center, would be:

(2R)(R sin60¨¬)/(sin30¨¬)(1/3)-[(¥ğR©÷)/6)(3)]

  Posted by josh_79_97 on 2005-08-01 21:50:45
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