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National and Regional Contests
Russia Contests
239 Open Math Olympiad
2009 239 Open Mathematical Olympiad
2
2
Part of
2009 239 Open Mathematical Olympiad
Problems
(1)
Equal distance from the Incenter
Source: 239 2009 J5
7/29/2020
On the sides
A
B
,
B
C
AB, BC
A
B
,
BC
and
C
A
CA
C
A
of triangle
A
B
C
ABC
A
BC
, points
K
,
L
K, L
K
,
L
and
M
M
M
are selected, respectively, such that
A
K
=
A
M
AK = AM
A
K
=
A
M
and
B
K
=
B
L
BK = BL
B
K
=
B
L
. If
∠
M
L
B
=
∠
C
A
B
\angle{MLB} = \angle{CAB}
∠
M
L
B
=
∠
C
A
B
, Prove that
M
L
=
K
I
ML = KI
M
L
=
K
I
, where
I
I
I
is the incenter of triangle
C
M
L
CML
CM
L
.
geometry
incenter