Question

Three circles are placed on a plane in such a way that each circle just touches the other two ,each having radius of 10 cm. find the area of region enclosed by them.

Answer 1

Answer:

Draw the triangle formed lines connecting the centers of the circles.

Then draw a line from the center of one circle that is tangent to the other circles.

Then the area of the triangle will be  R * h  where h is the height of the triangle.

R^2 + h*2 = (2 R)^2      and h^2 = 3 R^2   and h = 3^1/2 * R

So At = 3 ^ 1/2 R * R = 3^1/2 R^2       area of the triangle drawn above

The area of the portion of  a circle enclosed the triangle  is

pi * R^2 / 6   since the triangle is an equilateral triangle

And there are 3 such areas with area Ac = pi * R^2 / 2

Then the area between the circles is A = At - Ac

A = (3^1/2 - pi / 2) * R^2 = .161 R^2