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What is the equation of circle with origin as centre and passing throush the vertices of an equilateral triangle whose median is of length 3a ?
The origin or the center of the circle must act as the centroid of the equilateral trianlge . So,it must divide the median int 2:1. So the distance of the vertex of the triangle form the center is 2a,which will act as the radius of the circle. So the equation must be x^2+y^2=4a^2
Hi Abhi,
Let r be the radius of the circle.
As median will pass through the centre of the circle, and median is divided in the ratio 2:1 at the centre (which would be the centroid).
So r = 2a.
Hence Eqn of Circle : x^2 + y^2 = (2a)^2.
Hope that helps.
Best Regards,
Ashwin (IIT Madras).
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