Question

The area of an equilateral triangle inscribed in the circle $x^2+y^2-2 x=0$ is :

• A. $\frac{3 \sqrt{3}}{2}$
• B. $\frac{3 \sqrt{3}}{4}$
• C. $\frac{3 \sqrt{3}}{8}$
• D. none

Answer 1

Answer: (B)

Coordinates of point $P$ will be $(\text{acos} 30$, a $\sin30 ) P$ lies on the circle,
$\Rightarrow a^2 \cos ^2 30+ a ^2 \sin ^2 30$
$=2 a \cos 30 $
$\Rightarrow a ^2=2 a\cos 30$
$\Rightarrow a =\sqrt{3}$
Area $=\frac{\sqrt{3} a ^2}{4}=\frac{3 \sqrt{3}}{4}$