Question

In the given figure, OPQR is a rhombus three of whose vertices on the circle with centre at O. If the area of the rhombus be $32\sqrt{3}$sq-cm, find the radius of the circle.

• A. 10
• B. 9
• C. 8
• D. 7

Answer 1

The correct option is C

8

Let the radius of the circle = r cm.
$\because$ OPQR is a rhombus, $\therefore$ OP = PQ = QR = RO
$\because$ OP=OR = OQ = radius $\therefore$ OP = OQ = PQ = r cm
$\therefore$ $\Delta$ OPQ is an equalateral triangle.
Now area of the rhombus =2 $\times$ (area of $\Delta$ OPQ)
= $2\times \frac{\sqrt{3}}{4}\times r^2$ = $\frac{\sqrt{3}}{2}{r}^2$
As per question, $\frac{\sqrt{3}}{2}{r}^2=32\sqrt{3}\Rightarrow r^2=64\Rightarrow$ r = 8 ($\because$ r>0)
$\therefore$ The required radius = 8 cm.