If no force acts at point B, the velocity is unchanged, and the particle arrives at point K at time t = 2Δ t. The areas of the triangles OAB and OBK are equal, because they share the same base (r AB) and height (r ⊥). If Δ r is parallel to r B, the triangles OBK and OBC are likewise equal, because they share the same base (r B) and the height is unchanged. In that case, the areas of the triangles OAB and OBC are the same, and the particle sweeps out equal areas in equal time. Conversely, if the areas of all such triangles are equal, then Δ r must be parallel to r B, from which it follows that F is a central force. Thus, a particle sweeps out equal areas in equal times if and only if F is a central force.