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National and Regional Contests
Switzerland Contests
Swiss NMO - geometry
2009.5
2009.5
Part of
Swiss NMO - geometry
Problems
(1)
IM bisects segment AD, incircle related
Source: Switzerland - Swiss MO 2009 p5
7/17/2020
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
≠
A
C
AB \ne AC
A
B
=
A
C
and incenter
I
I
I
. The incircle touches
B
C
BC
BC
at
D
D
D
. Let
M
M
M
be the midpoint of
B
C
BC
BC
. Show that the line
I
M
IM
I
M
bisects segment
A
D
AD
A
D
.
geometry
bisects segment
incenter
incircle