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The equation of circumcircle of an equil...

The equation of circumcircle of an equilateral triangle is `x^2+y^2+2gx+2fy+c=0` and one vertex of the triangle is (1,1).The equation of incircle of the triangle is

A

`4(x^2+y^2)=g^2+f^2`

B

`4(x^2+y^2)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f)`

C

`4(x^2+y^2)+8gx+8fy=g^2+f^2`

D

none of these

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The equation of the circumcircle of an equilateral triangle is x^2+y^2+2gx+2fy+c=0 and one vertex of the triangle in (1, 1). The equation of the incircle of the triangle is a. 4(x^2+y^2)=g^2+f^2 b. 4(x^2+y^2)+8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f) c. 4(x^2+y^2)+8gx+8fy=g^2+f^2 d. None of These

The equation of circum circle of an equilateral triangle is x^2+y^2+2gx+2fy+c=0 .Find the area of the triangle.

Knowledge Check

  • The incentre of an equilateral triangle is ( 1, 1) and the equation of the one side is 3x + 4y + 3 = 0 . Then the equation of the circumcircle of the triangle is

    A
    `x^2+y^2-2x-2y-2 = 0`
    B
    `x^2+y^2-2x-2y-14 = 0`
    C
    `x^2+y^2-2x-2y+ 2 = 0`
    D
    `x^2+y^2-2x-2y+ 14 = 0`

  • The incentre of an equilateral triangle is (1,1) and the equation of one side is 3x + 4y + 3 = 0 . Then the equation of the circumcircle of the triangle is _

    A
    `x^(2) + y^(2) = - 2x - 2y - 2 = 0 `
    B
    `x^(2) + y^(2) - 2x - 2y - 14 = 0 `
    C
    `x^(2) + y^(2) - 2x - 2y + 2 = 0 `
    D
    `x^(2) + y^(2) - 2x - 2y + 14 = 0 `

  • If the equation of the base of an equilateral triangle is 2x - y=1 and the vertex is (-1,2), then the length of a side of the triangle is-

    A
    `(2)/(sqrt15)`
    B
    `(2sqrt2)/(sqrt15)`
    C
    `2sqrt((5)/(3))`
    D
    `sqrt5`

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    The equation of one arm of a equilateral triangle is x + y = 2 and the co-ordinate of the vertex opposite to this arm is (2, -1). Find the length of one arm of this triangle.

    If the equation of the side BC of an equilateral triangle ABC is x+y=2 and the coordinate of the vertex A is (2,3) then find the equation of the other two sides.

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