If the incentre of an equilateral triangle is 1 , 1 and the equation of its one side is 3 x + 4 y + 3 = 0 , then the equation of the circumcircle of this triangle is:

Question

If the incentre of an equilateral triangle is 1 , 1 and the equation of its one side is 3 x + 4 y + 3 = 0 , then the equation of the circumcircle of this triangle is:, x 2 + y 2 - 2 x - 2 y - 2 = 0, x 2 + y 2 - 2 x - 2 y + 2 = 0, x 2 + y 2 - 2 x - 2 y - 7 = 0, x 2 + y 2 - 2 x - 2 y - 14 = 0

MARKS App · Accepted Answer

3 x + 4 y + 3 = 0 Since, for equilateral triangle centroid in center and circumcenter is the same therefore length of A B = 3 1 + 4 1 + 3 3 2 + 4 2 = 10 5 = 2 R = 2 A B = 4 As centroid divide median in the ratio 2 : 1 Centre of the circle would be 1 , 1 ∴ Answer is x 2 + y 2 - 2 x - 2 y - 14 = 0

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