All lines UV pass through a fixed point
Source: Austrian Federal Competition 2011, part 2, #6
June 6, 2011
geometrygeometric transformationhomothetygeometry proposed
Problem Statement
Two circles and with radii and touch each outside at point . The other endpoints of the diameters through are on and on .
We choose two points and , one on each of the arcs of . ( is a convex quadrangle.)
Further, let be the second point of intersection of the line with and let be the second point of intersection of the line with .
The lines and intersect in and the lines and intersect in .
Show that there is a point that lies on all of these lines .