Question

If the radius of each circle in the image is 6 cm, what is the area (in cm2) of the quadrilateral formed by joining the centres of the circles?
​

Answer 1

Answer:

2√3 cm^2

Let O be the center of a circle whose radius OA = 6 cm.

Its area = πr^2 = π(6)^2 = 36πcm^2

Now, the area of this circle is trisected by two

concentric circles having radii OB and OC respectively.

∴ Area of the smallest circle ( with radius OC)

= 36π/3 cm^2

⇒π × OC^2 = 12π ⇒OC^2 = 12

⇒OC = 2√3 cm