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International Contests
Nordic
1996 Nordic
3
3
Part of
1996 Nordic
Problems
(1)
circle with diameter the altitude
Source: Nordic Mathematical Contest 1996 #3
10/4/2017
The circle whose diameter is the altitude dropped from the vertex
A
A
A
of the triangle
A
B
C
ABC
A
BC
intersects the sides
A
B
AB
A
B
and
A
C
AC
A
C
at
D
D
D
and
E
E
E
, respectively
(
A
≠
D
,
A
≠
E
)
(A\ne D, A \ne E)
(
A
=
D
,
A
=
E
)
. Show that the circumcenter of
A
B
C
ABC
A
BC
lies on the altitude drawn from the vertex
A
A
A
of the triangle
A
D
E
ADE
A
D
E
, or on its extension.
geometry
altitude