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) (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.
^2\left(\frac{\pi}{3}\right)\right))
You just need to simplify but I would leave the answer in terms of the radical and 
John
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