Question:
three circles are place on a plane in such a way that ech circle just touches the other two each of having the radius 10c. find the area enclosed by them
Answer:
Given radius of the circle is 10
Now, from the figure, ABC is an equilateral triangle.
So, ∠A = ∠B = ∠C = 60
and AB = BC = CA = 20 cm
Now, there are three sectors having angle 60
Now, area of the triangle ABC = √3/4 (side)2
= (√3/4)*(20)2
= (1.732*20*20)/4
= 1.732*20*5
= 173.2
Again area of the 3 sectors = 3* (60/360)*πr2
= 3* (1/6)*πr2
= π(10)2 /2
= (3.14*100)/2
= (314)/2
= 157
Now, area of the dotted region = area of the trinagle - area of the 3 sectors
= 173.2 - 157
= 16.2 cm2
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