Question

Find the area of circle in sq. cms, in which the chord of length 18 cm is at the distance of half of the radius of circle from the centre of circle:

• A. $108\pi$
• B. $54\pi$
• C. $27\pi$
• D. $81\pi$

Answer 1

Answer: (A)

Let the radius of circle be $r$

Given that distance between center of circle and the chord is $\frac{r}{2}$

So we get $9^2+(\frac{r}{2}{)}^2=r^2$

$\Rightarrow \frac{3r^2}{4}=81$

$\Rightarrow r^2=27\times 4=108$

Therefore the area of circle is $\pi r^2=108\pi$

So the correct option is $A$