Question

There are 3 circles touching each other. There is a triangle , the vertices of which are the centre of the circle. The triangle is equilateral with side length a. Find the area between all the circles

Answer 1

There are 3 circles with centers A,B,C.
Area of one circle(A) = πr^2
Area of another circle (B)=πr^2
Area of another circle (C)=πr^2

SUM OF THE AREAS OF 3 TRIANGLE'S ARE :-πr^2+πr^2+πr^2
=3πr^2

Now area of the triangle ABC= √3/4a^2

Area between all the circles = (SUM OF THE AREAS OF 3 TRIANGLE'S) -- (area of the triangle ABC)=

(3πr^2-√3/4a^2)