Question

The area of a circle whose radius is $6$ cm is trisected by two concentric circles. The radius of the smallest circle is

• A. $2\sqrt{3}$ cm
• B. $2\sqrt{6}$ cm
• C. $2$ cm
• D. $3$ cm

Answer 1

The correct option is A $2\sqrt{3}$ cm

Let O be the center of a circle whose radius OA = $6$ cm.
Its area = $\pi r^2=\pi (6{)}^2=36\pi c{m}^2$
Now, the area of this circle is trisected by two
concentric circles having radii OB and OC respectively.

$\therefore$ Area of the smallest circle ( with radius OC)

$=\frac{36\pi }{3}c{m}^2$

$\Rightarrow \pi \times O{C}^2=12\pi \Rightarrow O{C}^2=12$

$\Rightarrow OC=2\sqrt{3}cm$