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All-Russian Olympiad
1989 All Soviet Union Mathematical Olympiad
489
489
Part of
1989 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 489 All Soviet Union MO 1989 3 incircles have a common tangent
Source:
8/13/2019
The incircle of
A
B
C
ABC
A
BC
touches
A
B
AB
A
B
at
M
M
M
.
N
N
N
is any point on the segment
B
C
BC
BC
. Show that the incircles of
A
M
N
,
B
M
N
,
A
C
N
AMN, BMN, ACN
A
MN
,
BMN
,
A
CN
have a common tangent.
geometry
incircle
common tangent
tangent