Vary Q on AB
Source: Cono Sur 2004 #2
November 18, 2015
geometrycono sur
Problem Statement
Given a circle and a point on its exterior, two tangents to the circle are drawn through , with and being the points of tangency. We take a point on the minor arc of . Let be the intersection of with the line perpendicular to that goes through , and let be the intersection of with the line perpendicular to that goes through .
Show that, by varying on the minor arc , all of the lines pass through the same point.