In triangle `A B C` , the equation of side `B C` is `x-y=0.` The circumcenter and orthocentre of triangle are (2, 3) and (5, 8), respectively. The equation of the circumcirle of the triangle is

The vertices of a triangle are A(3, 7), B(3, 4) and C(5, 4). The equation of the bisector of the angle /_ABC is

If the coordinates of the vertices of triangle A B C are (-1,6),(-3,-9) and (5,-8) , respectively, then find the equation of the median through Cdot

If the middle points of the sides B C ,C A , and A B of triangle A B C are (1,3),(5,7), and (-5,7), respectively, then find the equation of the side A Bdot

In triangle A B C , the equation of the right bisectors of the sides A B and A C are x+y=0 and y-x=0 , respectively. If A-=(5,7) , then find the equation of side B Cdot

The mid points of the sides of a triangle are (5, 0), (5, 12) and (0, 12). The orthocentre of this triangle is

If a vertex, the circumcenter, and the centroid of a triangle are (0, 0), (3,4), and (6, 8), respectively, then the triangle must be (a)   a right-angled triangle (b)   an equilateral triangle (c)   an isosceles triangle (d)   a right-angled isosceles triangle

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

In triangle A B C ,/_A=60^0,/_B=40^0,a n d/_C=80^0dot If P is the center of the circumcircle of triangle A B C with radius unity, then the radius of the circumcircle of triangle B P C is (a)1 (b) sqrt(3) (c) 2 (d) sqrt(3) 2

Prove that the distance between the circumcenter and the orthocentre of triangle ABC is Rsqrt(1-8cosAcosBcosC)

The distance between the circumcenter and the orthocentre of the triangle whose vertices are (0,0),(6,8), and (-4,3) is Ldot Then the value of 2/(sqrt(5))L is_________