Question

Four equal circles each of radius a, touch each other. Show that area between them is (6/7)a².

Answer 1

Let circles be with centres A, B, C, D

Join A, B, C and D then ABCD is square formed with side = (a + a) = 2a

Radius = a

Area between circles = area of square – 4(area of quadrant)

(shaded region)

= (2a)²−4(1/4 area of circle with radius ′a′)