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

JEE Main 2015 Mathematics question

If the incentre of an equilateral triangle is and the equation of its one side is , then the equation of the circumcircle of this triangle is:

(1)
(2)
(3)
(4)Correct

Answer: (4)

Solution

In an equilateral triangle the incentre, circumcentre, centroid and orthocentre all coincide, so the circumcentre is also . The inradius is the perpendicular distance from this point to the given side:

r = = = 2.

For an equilateral triangle the circumradius is

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Question ID VK-115385