Circumcentre:

The point of intersection of the perpendicular bisectors of the sides of a triangle is called its circumcenter.

It is equidistance from the vertices of a triangle.

Let O is the circumcentre of a triangle ABC, then

OA = OB = OC and OA is called the circumradius.

To find the circumcentre of triangle ABC, we use the relation OA = OB = OC.

This gives two simultaneous linear equations and their solution gives the coordinate of the circumcentre.

Orthocentre:

The point of intersection of the altitude of a triangle is called its orthocentre.

To find the orthocentre, we first find equations of lines passing through vertices and perpendicular to the opposite sides.

Now, solving any two of these three equations, we get the coordinate of the orthocentre.