Collinear points - BxMO 2010
Source:
May 2, 2010
geometrygeometry proposed
Problem Statement
On a line there are three different points , and in that order. Let be the line through perpendicular to , and let be the line through perpendicular to . A line through , not coinciding with , intersects in and in . The line through perpendicular to intersects in and in . The line through perpendicular to intersects in and in .
(a) Prove that , , are collinear.
(b) Prove that , , are collinear.(2nd Benelux Mathematical Olympiad 2010, Problem 3)