`(1,-3,1),(2,-1,3),(0,1,2)` are vertices of a triangle then its orthocentre and circumcentre are situated at a distance of

If A(0,1,2) B(2,-1,3) and C(1,-3,1) are the vertices of a triangle then the distance between circumcentre and orthocentre is

The distance between orthocentre and circumcentre of an equilateral triangle is a) 1 b) 0 c) s d) 2 Delta

Assertion (A): If (-1,3,2) and (5,3,2) are respectively the orthocentre and circumcentre of a triangle, then (3,3,2) is its centroid. Reason (R): Centroid of a triangle divides the line segment joining the orthocentre and the circumcentre in the ratio 1:2 ,

If z_(1),z_(2)andz_(3) are the affixes of the vertices of a triangle having its circumcentre at the origin. If zis the affix of its orthocentre, prove that Z_(1)+Z_(2)+Z_(3)-Z=0.

Statement 1: If in a triangle, orthocentre, circumcentre and centroid are rational points, then its vertices must also be rational points. Statement : 2 If the vertices of a triangle are rational points, then the centroid, circumcentre and orthocentre are also rational points.

If A(0,2,3) , B=(2,-1,5) are two vertices of triangle ABC whose orthocentre is H . Then distance between the orthocentres of triangle HAC and triangle HBC is

The distance between the orthocentre and circumcentre of the triangle with vertices (0,0),(4,0),(0,6) is