The combined equation of three sides of a triangle is `(x^2-y^2)(2x+3y-6)=0` . If `(-2,a)` is an interior point and `(b ,1)` is an exterior point of the triangle, then (a)`2 < a < (10)/3` (b) `-2 < a < (10)/3` (c)`-1< b < 9/2` (d) `-1< b < 1`

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 equations of the sides of a triangle are x+y-5=0, x-y+1=0, and y-1=0. Then the coordinates of the circumcenter are

The equations of two sides of a triangle are 3y-x-2=0a n dy+x-2=0. The third side, which is variable, always passes through the point (5,-1) . Find the range of the values of the slope of the third side, so that the origin is an interior point of the triangle.

The sides of a triangle are the straight lines x+y=1,7y=x , and sqrt(3)y+x=0 . Then which of the following is an interior point of the triangle? (a)Circumcenter (b) Centroid (c)Incenter (d) Orthocenter

Find the lines whose combined equation is 6x^2+5x y-4y^2+7x+13 y-3=0

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

If the extremities of the base of an isosce- les triangle are the points (2a, 0) and (0,a) and the equation of one of the sides is x=2a, then the area of the triangle is

The equation of the base BC of an equilateral triangle ABC is x+y= 2 and A is (2, -1). The length of the side of the triangle is