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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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The solution | Comment 17 of 18 |

When the 3 circles touch each other externally and have the same radius r then on joining their centres we get an equilateral triangle whose sides are 2r. The area of the equilateral triangle is (2(3^1/2)r^2).Since it is an equilateral triangle so all the angles are 60.So all the sectors have angle 60 between them and all are equal in area. Therefore the area of the three sectors is       ((r^2)/6)*3.Therefore the area of the figure is                       (2(3^(1/2))r^2)-((r^2)/2).

  Posted by akash on 2005-12-31 12:09:42
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