MathDB
Common chord bisects segment

Source: China TSTST 3 Day 1 Q2

March 18, 2017
geometrypedal trianglecircumcircleorthocenterChina TST

Problem Statement

Let ABCDABCD be a non-cyclic convex quadrilateral. The feet of perpendiculars from AA to BC,BD,CDBC,BD,CD are P,Q,RP,Q,R respectively, where P,QP,Q lie on segments BC,BDBC,BD and RR lies on CDCD extended. The feet of perpendiculars from DD to AC,BC,ABAC,BC,AB are X,Y,ZX,Y,Z respectively, where X,YX,Y lie on segments AC,BCAC,BC and ZZ lies on BABA extended. Let the orthocenter of △ABD\triangle ABD be HH. Prove that the common chord of circumcircles of △PQR\triangle PQR and △XYZ\triangle XYZ bisects BHBH.
Back to ProblemsView on AoPS