Question

In the given figure OABC is a rhombus, three of whose vertices lie on a circle with center O.

If the area of the rhombus is $50\sqrt{3}c{m}^2$, then the area of the circle

is _____ sq cm. (Take $\pi =3.14$)

• A. 31.4
• B. 300
• C. 314
• D. 341

Answer 1

The correct option is C

314

Join OB

we know OA = OC = OB

(radius of same circle)

Also, OA = AB = BC = CO

(ABCD is a rhombus )

Hence the rhombus can be divided

into two equilateral $△$'s

Area of Rhombus = $2(\frac{\sqrt{3}}{4}\times r^2)$

$50\text{/}\sqrt{3}=\text{/}2\left(\frac{\sqrt{3}}{\text{/}{4}_2}\right)r^2$

$r^2=100\Rightarrow r=10cm$

Area of circle = $\pi r^2$

=$\left(3.14\right)\left(100\right)$

=$314c{m}^2$