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Contests
National and Regional Contests
Italy Contests
ITAMO
2019 ITAMO
5
5
Part of
2019 ITAMO
Problems
(1)
Midpoint of the internal bisector
Source: ITAMO 2019 #5
5/3/2019
Let
A
B
C
ABC
A
BC
be an acute angled triangle
.
.
.
Let
D
D
D
be the foot of the internal angle bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
and let
M
M
M
be the midpoint of
A
D
.
AD.
A
D
.
Let
X
X
X
be a point on segment
B
M
BM
BM
such that
∠
M
X
A
=
∠
D
A
C
.
\angle MXA=\angle DAC.
∠
MX
A
=
∠
D
A
C
.
Prove that
A
X
AX
A
X
is perpendicular to
X
C
.
XC.
XC
.
geometry
ITAMO 2019