Circle with center I, inscribed in a triangle ABC , touches the sides BC and AC at points A1 and B1 respectively. On rays A1I and B1I, respectively, let be the points A2 and B2 such that IA2=IB2=R, where Ris the radius of the circumscribed circle of the triangle ABC. Prove that:
a) AA2=BB2=OI where O is the center of the circumscribed circle of the triangle ABC,
b) lines AA2 and BB2 intersect on the circumcircle of the triangle ABC. geometryincirclecircumcircle