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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.

Yousif.m  May 17, 2018
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Guest May 17, 2018

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