MathDB
Vary Q on AB

Source: Cono Sur 2004 #2

November 18, 2015
geometrycono sur

Problem Statement

Given a circle CC and a point PP on its exterior, two tangents to the circle are drawn through PP, with AA and BB being the points of tangency. We take a point QQ on the minor arc ABAB of CC. Let MM be the intersection of AQAQ with the line perpendicular to AQAQ that goes through PP, and let NN be the intersection of BQBQ with the line perpendicular to BQBQ that goes through PP. Show that, by varying QQ on the minor arc ABAB, all of the lines MNMN pass through the same point.