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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 ______.
Options
x2 + y2 = 9a2
x2 + y2 = 16a2
x2 + y2 = 4a2
x2 + y2 = a2
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Solution
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 = `2/3` AD = `2/3 xx 3a = 2a`
∴ The equation of the circle is (x – 0)2 + (y – 0)2 = (2a)2
⇒ x2 + y2 = 4a2
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