Question

The centroid of an equilateral triangle is \( (0,0) \) and the length of the altitude is 6. The equation of the circumcircle of the triangle is 

1) \( x^{2}+y^{2}=6 \) 

2) \( x^{2}+y^{2}=16 \) 

3) \( x^{2}+y^{2}=9 \) 

4) \( x^{2}+y^{2}=36 \)

Answer 1

Correct option is 2) x² + y² = 16.

\(\therefore x_1 + x_2 + x_3 = 0\)

& \(y_1 + y_2 + y_3 = 0\)

\((2x_3 - (x_1 + x_2)) ^2 + (2y_3 - (y_1 + y_2))^2 = 144\)

⇒ \((3x_3)^2 + (3y_3)^2 = 144\)

⇒ \({x_3}^2 + {y_3}^2 = \frac{144}9 = 16\)

\(\therefore \) Equation of circumcircle is \(x^2 + y^2 = 16.\)