The area of an equilateral triangle inscribed in the circle x2+y2-2 x=0 is :

Question

The area of an equilateral triangle inscribed in the circle x2+y2-2 x=0 is : (A) (3 √3/2) (B) (3 √3/4) (C) (3 √3/8) (D) none

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/eab143315bdfe412abb0727f20f96d75-.png" /> Coordinates of point P will be ( textacos 30, a sin30 ) P lies on the circle, ⇒ a2 cos 2 30+ a 2 sin 2 30 =2 a cos 30 ⇒ a 2=2 a cos 30 ⇒ a =√3 Area =(√3 a 2/4)=(3 √3/4)

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

$\frac{3 3}{2}$

$\frac{3 3}{4}$

$\frac{3 3}{8}$

none

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

Q. The area of an equilateral triangle inscribed in the circle x2+y2−2x=0 is :

233​​

433​​

833​​