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Austria Contests
Austrian MO Beginners' Competition
2018 Austria Beginners' Competition
2
2
Part of
2018 Austria Beginners' Competition
Problems
(1)
AM = AF iff <BAC = 60^o
Source: Austria Beginners' Competition 2018 p2
2/24/2020
Let
A
B
C
ABC
A
BC
be an acute-angled triangle,
M
M
M
the midpoint of the side
A
C
AC
A
C
and
F
F
F
the foot on
A
B
AB
A
B
of the altitude through the vertex
C
C
C
. Prove that
A
M
=
A
F
AM = AF
A
M
=
A
F
holds if and only if
∠
B
A
C
=
6
0
o
\angle BAC = 60^o
∠
B
A
C
=
6
0
o
.(Karl Czakler)
geometry
equal segments
midpoint
altitude