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2017 APMO
2
2
Part of
2017 APMO
Problems
(1)
APMO 2017: (ADZ) passes through M
Source: APMO 2017, problem 2
5/14/2017
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
<
A
C
AB < AC
A
B
<
A
C
. Let
D
D
D
be the intersection point of the internal bisector of angle
B
A
C
BAC
B
A
C
and the circumcircle of
A
B
C
ABC
A
BC
. Let
Z
Z
Z
be the intersection point of the perpendicular bisector of
A
C
AC
A
C
with the external bisector of angle
∠
B
A
C
\angle{BAC}
∠
B
A
C
. Prove that the midpoint of the segment
A
B
AB
A
B
lies on the circumcircle of triangle
A
D
Z
ADZ
A
D
Z
.Olimpiada de Matemáticas, Nicaragua
geometry
APMO