Question

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 ______.

पर्याय

• x² + y² = 9a²

• x² + y² = 16a²

• x² + y² = 4a²

• x² + y² = a²

Answer 1

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 x² + y² = 4a².

Explanation:

Let ABC be an equilateral triangle in which median AD = 3a.

Centre of the circle is same as the centroid of the triangle

i.e., (0, 0)

AG : GD = 2 : 1

So, AG = ${\displaystyle \frac{2}{3}}$ AD = ${\displaystyle \frac{2}{3}\times 3a=2a}$

∴ The equation of the circle is (x – 0)² + (y – 0)² = (2a)²

⇒ x² + y² = 4a²