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2016 Balkan MO Shortlist
G1
G1
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2016 Balkan MO Shortlist
Problems
(1)
Bulgarian National Olympiad 2018 Day 2 P4
Source:
4/15/2018
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral ,circumscribed about a circle. Let
M
M
M
be a point on the side
A
B
AB
A
B
. Let
I
1
I_{1}
I
1
,
I
2
I_{2}
I
2
and
I
3
I_{3}
I
3
be the incentres of triangles
A
M
D
AMD
A
M
D
,
C
M
D
CMD
CM
D
and
B
M
C
BMC
BMC
respectively. Prove that
I
1
I
2
I
3
M
I_{1}I_{2}I_{3}M
I
1
I
2
I
3
M
is circumscribed.
geometry