Question

In the above figure, if $OA=x$ and $\angle AOB={120}^{\circ }$, find the length of chord $AB$ in terms of $x$.

• A. $\sqrt{2}x$
• B. $\sqrt{3}x$
• C. $\frac{x}{\sqrt{2}}$
• D. $\frac{x}{\sqrt{3}}$

Answer 1

The correct option is B $\sqrt{3}x$

Let the length of chord AB be $a$ units.

Using cosine rule we get,

$\cos 120=\frac{x^2+x^2-a^2}{2x^2}$

$-\frac{1}{2}=\frac{2x^2-a^2}{2x^2}$

$-x^2-2x^2=-a^2$

$a=x\sqrt{3}$

Hence, length of chord AB is $x\sqrt{3}$ units.