Question

An equilateral triangle is inscribed in the circle $x^2+y^2=a^2$ with the vertex at $(a,0)$. The equation of the side opposite to this vertex is

• A. $2x-a=0$
• B. $x+a=0$
• C. $2x+a=0$
• D. $3x-2a=0$

Answer 1

Answer: (C)

$2x+a=0$

$A(a,0)$ be the vertex of the equilateral triangles $ABC$ inscribed in the circle $x^2+y^2=a^2$
Let $M$ be the middle point of the side $BC$

then $MOA$ is perpendicular to $BC$ and $0$

being the centroid of the triangle $OA=2\left(OM\right)$
So if $(h,k)$ be the coordinates of $M$
then $\frac{2h+a}{3}=0$ and $\frac{2k+0}{3}=0$
$\Rightarrow h=-\left(a/2\right)$ and $k=0$ and

Hence the equation of $BC$ is $x=-a/2$$\Rightarrow 2x+a=0$