1. Two circles with centres N and S and radii a and c (where a < c) respectively touch externally at P. ABC and ADE are common tangents to the two circles. Prove that A, N and P are collinear.
2. Consider the diagram below:
MN is a chord of fixed length in a circle; Q is a point on the major arc MN. The bisectors of MNQ and NMQ meet the circle at A and B respectively. Prove that the distance between A and B is constant even when Q moves.