Question

Choose the correct alternative:

The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3a is

Options

• x² + y² = 9a² 

• x² + y² = 16a² 

• x² + y² = 4a² 

• x² + y² = a² 

Answer 1

x² + y² = 4a² 

Explanation;

Since the triangle is equilateral.

∴ The centroid of the triangle is same as the circumcentre;

and radius of the circumcircle = `2/3("median")`

= `2/3(3"a")`

= 2a

Hence, the equation of the circumcircle whose centre is at (0, 0) and radius 2a is x² + y² = 4a².