MathDB

i hope I translated it ok (didn´t solve it)

Source: Romanian District Olympiad 2016, Grade IX, Problem 1

October 4, 2018

geometryvector

Problem Statement

Let

ABCD

be a sqare and

E

be a point situated on the segment

BD,

but not on the mid. Denote by

H

and

K

the orthocenters of

ABE,

respectively,

ADE.

Show that

\overrightarrow{BH}=\overrightarrow{KD} .