MathDB
Problems
Contests
National and Regional Contests
Malaysia Contests
JOM Shortlists
JOM 2015 Shortlist
G1
G1
Part of
JOM 2015 Shortlist
Problems
(1)
OEHF is parallelogram
Source: Junior Olympiad of Malaysia Shortlist 2015 G1
7/17/2015
Given a triangle
A
B
C
ABC
A
BC
, and let
E
E
E
and
F
F
F
be the feet of altitudes from vertices
B
B
B
and
C
C
C
to the opposite sides. Denote
O
O
O
and
H
H
H
be the circumcenter and orthocenter of triangle
A
B
C
ABC
A
BC
. Given that
F
A
=
F
C
FA=FC
F
A
=
FC
, prove that
O
E
H
F
OEHF
OE
H
F
is a parallelogram.
geometry
parallelogram