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Canada National Olympiad
1994 Canada National Olympiad
5
5
Part of
1994 Canada National Olympiad
Problems
(1)
Prove angles are equal
Source: Canadian Mathematical Olympiad - 1994 - Problem 5.
5/13/2011
Let
A
B
C
ABC
A
BC
be an acute triangle. Let
A
D
AD
A
D
be the altitude on
B
C
BC
BC
, and let
H
H
H
be any interior point on
A
D
AD
A
D
. Lines
B
H
,
C
H
BH,CH
B
H
,
C
H
, when extended, intersect
A
C
,
A
B
AC,AB
A
C
,
A
B
at
E
,
F
E,F
E
,
F
respectively. Prove that
∠
E
D
H
=
∠
F
D
H
\angle EDH=\angle FDH
∠
E
DH
=
∠
F
DH
.
trigonometry
geometry proposed
geometry
Canada
angles
Triangle