Question

If three circles of radius A each are drawn such that each touches the other two,prove that area included between them is equal to 4/25 a^2​

Answer 1

Answer:

Step-by-step explanation:

According to question

Radius of each circle = a

Let the center of three circles be A, B and C

Thus joining the three circles we get a triangle ABC

in which

AB = BC = AC = 2a

Angle of triangle in each circle = 60 deg

Thus      

Are of each arc = pi/3 a^2

So are of three arcs = pi a^2

Also area of triangle ABC = root 3/4  (2a)^2

                                         = root 3  a^2

Thus Area left = root 3   a^2 - pi   a^2

                       = 3.14 - 1.73 a^2

                       = 1.41 a^2