Question

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

$\frac{3\sqrt{3}}{4}$

Coordinates of point $P$ will be $(a\cos {30}^o,a\sin {30}^o)$ lie on the circle.
$\Rightarrow$ $a^2{\cos }^2{30}^o+a^2{\sin }^o{30}^o$$=2a\cos {30}^o$
$\Rightarrow$ $a=\sqrt{3}$
$\therefore$ Area$=\frac{\sqrt{3}{a}^2}{4}=\frac{3\sqrt{3}}{4}$