MathDB
A quadrilateral and some Simson and Euler lines

Source: Romania TST 1 2012, Problem 2

May 3, 2012
Eulergeometrycircumcircleparallelogramgeometric transformationreflectioncyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral such that the triangles BCDBCD and CDACDA are not equilateral. Prove that if the Simson line of AA with respect to △BCD\triangle BCD is perpendicular to the Euler line of BCDBCD, then the Simson line of BB with respect to △ACD\triangle ACD is perpendicular to the Euler line of △ACD\triangle ACD.
Back to ProblemsView on AoPS