The vertices of a triangle are O (0,0) , A(a,0) and B (0,b). Write the coordinates of the circumcentre. and also Please explain what is a circumcentre.

circumcentre is the point of intersection of the perpendicuar bisectors of a triangle. 

the coordinates o(0,0) , A(a,0) , B(0,b) form a right triangle.

In the special case of a right triangle, the circumcenter  lies exactly at the midpoint of the hypotenuse (longest side).

so, in this case, the coordinates of circuumcentre are (a/2,b/2).

approve my answer if u like it......:))

circumcentre=centre of circle circumscribing a triangle

here circumcentre is(a/2,b/2)