SOLUTION: Three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these circles.

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Question 240236: Three circles each of radius 3.5 cm are drawn in such a way that each of them
touches the other two. Find the area enclosed between these circles.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


If the circles just touch each other, then you can draw a line connecting the centers of each pair of adjacent circles creating an equilateral triangle of side length 7 (2 times 3.5). The area of an equilateral triangle is given by:



There are four areas inside of this equilateral triangle, three circle sectors and the area we seek.

The area of a circle sector is given by:



where is the central angle of the sector.

So, the area we want is the area of the equilateral triangle minus three times the sector area.




You just need to simplify but I would leave the answer in terms of the radical and

John