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Question
If the centroid of an equilateral triangle is (1, 1) and its one vertex is (−1, 2), then the equation of its circumcircle is
Options
x2 + y2 − 2x − 2y − 3 = 0
x2 + y2 + 2x − 2y − 3 = 0
x2 + y2 + 2x + 2y − 3 = 0
none of these
Solution
x2 + y2 − 2x − 2y − 3 = 0
The centre of the circumcircle is (1, 1).
Radius of the circumcircle = \[\sqrt{\left( 1 + 1 \right)^2 + \left( 1 - 2 \right)^2} = \sqrt{5}\]
∴ Equation of the circle: \[\left( x - 1 \right)^2 + \left( y - 1 \right)^2 = 5\]
\[\Rightarrow x^2 + y^2 - 2x - 2y - 3 = 0\]
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