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International Contests
APMO
2007 APMO
2
2
Part of
2007 APMO
Problems
(1)
an acute angled triangle with $\angle{BAC}=60^0$
Source: APMO 2007
3/31/2007
Let
A
B
C
ABC
A
BC
be an acute angled triangle with
∠
B
A
C
=
6
0
∘
\angle{BAC}=60^\circ
∠
B
A
C
=
6
0
∘
and
A
B
>
A
C
AB > AC
A
B
>
A
C
. Let
I
I
I
be the incenter, and
H
H
H
the orthocenter of the triangle
A
B
C
ABC
A
BC
. Prove that
2
∠
A
H
I
=
3
∠
A
B
C
2\angle{AHI}= 3\angle{ABC}
2∠
A
H
I
=
3∠
A
BC
.
geometry
incenter