In the triangle ABC, ∠B is greater than ∠C. T is the midpoint of the arc BAC from the circumcircle of ABC and I is the incenter of ABC. E is a point such that \angle AEI\equal{}90^\circ and AE∥BC. TE intersects the circumcircle of ABC for the second time in P. If \angle B\equal{}\angle IPB, find the angle ∠A. geometrycircumcircleincentergeometry proposed