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?

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       (¥ð(r^2)/6)*3.Therefore the area of the figure is                       (2(3^(1/2))r^2)-(¥ð(r^2)/2).

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