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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
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Solution
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.
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