Question

An equilateral triangle whose circumcentre is (-2, 5) one side is on y- axis then length of side of triangle is-

• A. 6
• B. $2\sqrt{3}$
• C. $4\sqrt{3}$
• D. 4

Answer 1

Answer: (C)

$4\sqrt{3}$

G divide median AD in $2:1$

$\Rightarrow \frac{AG}{GD}=\frac{2}{1}$

$\Rightarrow AG=4$

$\Rightarrow AD=6$

In $\Delta ABD,\tan 60=\frac{AD}{DB}$

$\Rightarrow BD=\frac{6}{\sqrt{3}}$

$\Rightarrow BC=\frac{2\times 6}{\sqrt{3}}=4\sqrt{3}$

$\Rightarrow \left(C\right)$.