In the coordinate plane, a point is called a lattice point if both of its coordinates are integers. Let $$A$$ be the point $$(12,84)$$. Find the number of right angled triangles $$ABC$$ in the coordinate plane where $$B$$ and $$C$$ are lattice points, having a right angle at the vertex $$A$$ and whose incenter is at the origin $$(0,0)$$.