Question

Four equal circles, each of radius a, touch each other. Show that the area between them is6/7a².(Take π=3.14)

Answer 1

Area  = (6/7)a² is proved

Step-by-step explanation:

Please refer to the attached diagram.

Let circles be with centers 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)

  = (2a)² − 4(1/4  πa²)

  = 4a² - πa²

  = a² (4 - 22/7)

  = a² (28-22)/7

  = (6/7)a²

Hence proved.