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Problems
Contests
National and Regional Contests
Argentina Contests
Argentina National Olympiad
2003 Argentina National Olympiad
4
4
Part of
2003 Argentina National Olympiad
Problems
(1)
area of triangle of circumcenters, right trapezoid related
Source: 2003 Argentina OMA L3 p4
6/16/2020
The trapezoid
A
B
C
D
ABCD
A
BC
D
of bases
A
B
AB
A
B
and
C
D
CD
C
D
, has
∠
A
=
9
0
o
,
A
B
=
6
,
C
D
=
3
\angle A = 90^o, AB = 6, CD = 3
∠
A
=
9
0
o
,
A
B
=
6
,
C
D
=
3
and
A
D
=
4
AD = 4
A
D
=
4
. Let
E
,
G
,
H
E, G, H
E
,
G
,
H
be the circumcenters of triangles
A
B
C
,
A
C
D
,
A
B
D
ABC, ACD, ABD
A
BC
,
A
C
D
,
A
B
D
, respectively. Find the area of the triangle
E
G
H
EGH
EG
H
.
geometry
trapezoid
right triangle
Circumcenter
area of a triangle