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Problems
Contests
National and Regional Contests
Mexico Contests
Mexico National Olympiad
1990 Mexico National Olympiad
6
6
Part of
1990 Mexico National Olympiad
Problems
(1)
similar triangles around a right triangle
Source: Mexican Mathematical Olympiad 1990 OMM P6
7/29/2018
A
B
C
ABC
A
BC
is a triangle with
∠
C
=
9
0
o
\angle C = 90^o
∠
C
=
9
0
o
.
E
E
E
is a point on
A
C
AC
A
C
, and
F
F
F
is the midpoint of
E
C
EC
EC
.
C
H
CH
C
H
is an altitude.
I
I
I
is the circumcenter of
A
H
E
AHE
A
H
E
, and
G
G
G
is the midpoint of
B
C
BC
BC
. Show that
A
B
C
ABC
A
BC
and
I
G
F
IGF
I
GF
are similar.
geometry
similar triangles
right triangle