MathDB

radical axis get spammed using humpty points

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

March 4, 2023

geometryhumpty pointsradical axisprojectionsothorcenterSharygin Geometry OlympiadSharygin 2023

Problem Statement

Let

ABCD

be a cyclic quadrilateral;

M_{ac}

be the midpoint of

AC

;

H_d,H_b

be the orthocenters of

\triangle ABC,\triangle ADC

respectively;

P_d,P_b

be the projections of

H_d

and

H_b

BM_{ac}

and

DM_{ac}

respectively. Define similarly

P_a,P_c

for the diagonal

BD

. Prove that

P_a,P_b,P_c,P_d

are concyclic.