Given a triangle ABC, let I be the point of intersection of the (interior) angle bisectors, bisector a of angle BAC and bisector b of angle ABC.

1. Prove that angle AIB is obtuse.
2. Prove that an exterior angle bisector of angle BAC cannot be parallel to line AI.

(c) Use (b) to explain why there must be 4 points of intersection of the interior and exterior angle bisectors of A, B, C.