MathDB

21

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

radical axis get spammed using humpty points

Source: Sharygin 2023 - P21 (Grade-10-11)

3/4/2023
Let ABCDABCD be a cyclic quadrilateral; MacM_{ac} be the midpoint of ACAC; Hd,HbH_d,H_b be the orthocenters of △ABC,△ADC\triangle ABC,\triangle ADC respectively; Pd,PbP_d,P_b be the projections of HdH_d and HbH_b to BMacBM_{ac} and DMacDM_{ac} respectively. Define similarly Pa,PcP_a,P_c for the diagonal BDBD. Prove that Pa,Pb,Pc,PdP_a,P_b,P_c,P_d are concyclic.
geometryhumpty pointsradical axisprojectionsothorcenterSharygin Geometry OlympiadSharygin 2023