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

Prove that the distance between the circumcenter and the incenter of triangle ABC is sqrt(R^2-2R r)

In Delta ABC it is given distance between the circumcentre (O) and orthocentre (H) is R sqrt(1-8 cos A cos B cos C) . If Q is the midopoint of OH, then AQ is

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_________

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_________

Find the distance between circumcentre and orthocentre of the triangle whose vertices are (0,0),(6,8) and (-4,3)

A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

A triangle is inscribed in a circle of radius 1. The distance between the orthocentre and the circumcentre of the triangle cannot be

Consider a pair of perpendicular straight lines ax^(2)+3xy-2y^(2)-5x+5y+c=0 . Distance between the orthocenter and the circumcenter of triangle ABC is

Consider a triangle PQR with coordinates of its vertices as P(-8,5), Q(-15, -19), and R (1, -7). The bisector of the interior angle of P has the equation which can be written in the form ax+2y+c=0. The distance between the orthocenter and the circumcenter of triangle PQR is