MathDB

KJMO 1998 P3 Homothety on orthocenter

Source: 1998 KJMO

June 30, 2024

geometrycircumcirclehomothetygeometric transformation

Problem Statement

O

is the circumcenter of

ABC

, and

H

is the orthocenter of

ABC

. If

D

is a midpoint of

AC

and

E

is the intersection of

BO

and

ABC

's circumcircle not

B

, show that three points

H, D, E

are collinear.