A person is going from point \(A\) to point \(B\) on a grid. He can either move one unit up or one unit to the right in one move, along the grid lines. The perimeter of the area in which he can move is given in the figure by a quarter circle of radius 10 centered at point \(C=(10, 0).\) Find the number of all possible paths assuming that he cannot cross the perimeter.
Clarification: He may be on the perimeter. He may not go outside the quarter circle.