Question

The area of cyclic quadrilateral $ABCD$ is $\frac{3\sqrt{3}}{4}$. The radius of the circle circumscribing it is $1$.If $AB=1$ $BC=\sqrt{3}$ then $\angle ABC$ is equal to ?

• A. $\pi /3$
• B. $\pi /2$
• C. $\pi /4$
• D. None of these

Answer 1

Answer: (A)

$\pi /3$

The area of quadrilateral is given as $AB\times BC\times \sin \left(\angle ABC\right)=\frac{3\sqrt{3}}{4}\sin B=\frac{3\sqrt{3}}{4}\times \frac{2}{3}\sin B=\frac{\sqrt{3}}{2}B=\pi /3$