MathDB
Parallelogram

Source: All-Russian 2011

May 17, 2011
geometryparallelogramcircumcirclegeometric transformationreflectionsymmetrygeometry proposed

Problem Statement

On side BCBC of parallelogram ABCDABCD (AA is acute) lies point TT so that triangle ATDATD is an acute triangle. Let O1O_1, O2O_2, and O3O_3 be the circumcenters of triangles ABTABT, DATDAT, and CDTCDT respectively. Prove that the orthocenter of triangle O1O2O3O_1O_2O_3 lies on line ADAD.