The equation of the in-circle of an equilateral triangle is `x^(2) + y^(2) + 2x - 4y - 8 = 0`, find the area of the equilateral triangle.

The equation of in circle of an equilateral triangle is 2x^(2) + 2y^(2) + 3x - y - 5 = 0 . Find the area of the triangle.

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

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 4(x^(2)+y^(2))=g^(2)+f^(2)4(x^(2)+y^(2))=8gx+8fy=(1-g)(1+3g)+(1-f)(1+3f)4(x^(2)+y^(2))=8gx+8fy=g^(2)+f^(2) none of these

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

Obtain the area of equilateral triangle inscribed in circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

Show that the lines x^(2) - 4xy + y^(2) = 0 and x + y = 10 contain the sides of an equilateral triangle.

The equation to the base of an equilateral triangle is 4x-3y+10=0 and its vertex is at (-2,-1), find the length of a side of the triangle.

Find the area of the equilateral triangle inscribed in the circle x^(2) + y^(2) - 4x + 6y - 3 = 0 .