What is the centroid of a right triangle?

The centroid of any triangle, right triangles included, is the point where the angle bisectors of all three vertices of a triangle intersect. Given a triangle made from a sufficiently rigid and uniform material, the centroid is the point at which that triangle balances.

The centroid of a triangle on a coordinate plane is found by taking the average position of the three vertices. For example, if the coordinates of the vertices of a right triangle are (0, 0), (15, 0) and (15, 15), the centroid is found by adding together the x coordinates, 0, 15 and 15, dividing by 3, and then performing the same operation for the y coordinates, 0, 0 and 15. The centroid of such a triangle is at the point (10, 5).