The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3 a isA. `x^(2)+y^(2)=9a^(2)`B. `x^(2)+y^(2)=16a^(2)`C. `x^(2)+y^(2)=4a^(2)`D. `x^(2)+y^(2)=a^(2)`

The equation of a circle with origin as centre and passing through the

1.	The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3 a isA. `x^(2)+y^(2)=9a^(2)`B. `x^(2)+y^(2)=16a^(2)`C. `x^(2)+y^(2)=4a^(2)`D. `x^(2)+y^(2)=a^(2)`
Answer» Correct Answer - C It is given that the triangle is equilateral . Therefore, centroid of the triangle is same as the circumcentre. Also, Radius of the circumcircle `=(2)/(3)`(Median)`=(2)/(3)(3a)=2a` Hence, the equation of the circumcircle whose centre is at (0, 0) and radius `2a, ` is `x^(2)+y^(2)=(2a)^(2)`.

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The equation of a circle with origin as centre and passing through the vertices of an equilateral triangle whose median is of length 3 a isA. `x^(2)+y^(2)=9a^(2)`B. `x^(2)+y^(2)=16a^(2)`C. `x^(2)+y^(2)=4a^(2)`D. `x^(2)+y^(2)=a^(2)`

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