The figure below shows an arbelos ABC (AB, BC, and AC are semicircles of centers O_{1}, O_{2}, and O). The incircle I of the arbelos is tangent to semicircles AC, AB, and BC at T, T_{1}, and T_{2}, respectively. IH is perpendicular to AC. Prove that AT_{2}, TB, CT_{1}, IH, and the incircle are concurrent at a point P.
