SOLUTION: Find the area contained between three circles of radius 20 cm. each of which is externally tangent to the other two.

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Question 1180141: Find the area contained between three circles of radius 20 cm. each of which is externally tangent to the other two.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Draw a sketch; then draw the segments connecting the centers of the three circles.

Those three segments will form an equilateral triangle with side length equal to twice the radius of the circles.

The area between the circles is the area of that equilateral triangle, minus the areas of the three "slices of pie" that are the intersections of the triangle and the three circles.

Area of an equilateral triangle with side length s: %28s%5E2%2Asqrt%283%29%29%2F4
Area of a circle with radius r: pi%2Ar%5E2

Note the angles of the equilateral triangle are each 60 degrees, which is 1/6 of a circle. So the combined areas of the three "slices of pie" is half the area of one of the circles.

You can fill in the details and do the calculations....

(your final answer should be about 64.5)