Question

Construct an equilateral triangle of side $6cm$. Construct the circumcentre of it. Then the measure of radius is :

• A. $4\sqrt{3}$
• B. $\sqrt{3}$
• C. $2\sqrt{3}$
• D. $3\sqrt{3}$

Answer 1

The correct option is C $2\sqrt{3}$

$\Rightarrow$ Draw a line segment $BC=6cm$

$\Rightarrow$ Take $B$ and $C$ as a center with radius $6cm$ and draw an arc meeting at point $A$.

$\Rightarrow$ Join $AB$ and $AC$. We get $ABC$ as the required equilateral triangle.

$\Rightarrow$ Draw a perpendicular bisector on sides $AB,BC,AC$ meeting at point $O$.

$\Rightarrow$ Take $O$ as the center with radius equal to $OA$ and draw a circle.

$\Rightarrow$ We have to measure radius of the circumcircle, i.e the measure of length of $OA$.

$\therefore$ Radius of circle is $3.5\approx 2\sqrt{3}$