Let AA1,BB1,CC1 be the heights of triangle ABC and H be its orthocenter. Liune ℓ parallel to AC, intersects straight lines AA1 and CC1 at points A2 and C2, respectively. Suppose that point B1 lies outside the circumscribed circle of triangle A2HC2. Let B1P and B1T be tangent to of this circle. Prove that points A1,C1,P, and T are cyclic. geometrycircumcircleConcyclicorthocenteraltitudes