The incentre of the triangle having its vertices at O (0, 0), A(5, 0) and B (0, 12) is

Clearly, ∆OAB is a right triangle right-angled at O such that OA= 5, OB=12 and AB= 13.So, the coordinates of incentre are13×0+5×0+12×513+5+12,13×0+5×12+12×013+5+12 i.e. (2,2)