If the centroid of an equilateral triangle is $(1, 1)$ and its one vertex is $(- 1, 2)$ then the equation of its circumcircle is

x^{2} + y^{2} - 2 x - 2 y - 3 = 0

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x^{2} + y^{2} + 2 x - 2 y - 3 = 0

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x^{2} + y^{2} + 2 x + 2 y - 3 = 0

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none of these

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Solution

The correct option is A $x^{2} + y^{2} - 2 x - 2 y - 3 = 0$
Given centroid of an equilateral triangle is $G (1, 1)$ .
We know that in an equilateral triangle, centroid, circumcenter and incenter are at the same point.
So, the circumcenter is at $G (1, 1)$ .
Given one vertex of equilateral triangle at $A (- 1, 2)$
So, circumradius $= A G = \sqrt{5}$
So, equation of circumcircle is
$(x - 1)^{2} + (y - 1)^{2} = 5$
$\Rightarrow x^{2} + y^{2} - 2 x - 2 y - 3 = 0$

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Similar questions

P (2, 2)

x^{2} + y^{2} = 1,

A

B .

△ P A B

c_{1} : x^{2} + y^{2} - 2 x - 2 y + 3 = 0

c_{2} : x^{2} - y^{2} - 2 x - 2 y + 7 = 0

C_{1} : x^{2} + y^{2} + 2 x - 3 = 0, C_{2} : x^{2} + y^{2} - 2 x - 3 = 0, C_{3} : x^{2} + y^{2} - 2 y - 3 = 0,

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