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Junior Balkan MO
2016 Junior Balkan MO
1
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Part of
2016 Junior Balkan MO
Problems
(1)
JBMO 2016 Problem 1
Source:
6/26/2016
A trapezoid
A
B
C
D
ABCD
A
BC
D
(
A
B
∣
∣
C
F
AB || CF
A
B
∣∣
CF
,
A
B
>
C
D
AB > CD
A
B
>
C
D
) is circumscribed.The incircle of the triangle
A
B
C
ABC
A
BC
touches the lines
A
B
AB
A
B
and
A
C
AC
A
C
at the points
M
M
M
and
N
N
N
,respectively.Prove that the incenter of the trapezoid
A
B
C
D
ABCD
A
BC
D
lies on the line
M
N
MN
MN
.
geometry
trapezoid
incenter