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Argentina Cono Sur TST
2012 Argentina Cono Sur TST
5
Argentina Cono Sur TST 2012. Problem 5
Argentina Cono Sur TST 2012. Problem 5
Source:
April 26, 2015
geometry
angle bisector
excenter
Problem Statement
Let
A
B
C
ABC
A
BC
be a triangle, and
K
K
K
and
L
L
L
be points on
A
B
AB
A
B
such that
∠
A
C
K
=
∠
K
C
L
=
∠
L
C
B
\angle ACK = \angle KCL = \angle LCB
∠
A
C
K
=
∠
K
C
L
=
∠
L
CB
. Let
M
M
M
be a point in
B
C
BC
BC
such that
∠
M
K
C
=
∠
B
K
M
\angle MKC = \angle BKM
∠
M
K
C
=
∠
B
K
M
. If
M
L
ML
M
L
is the angle bisector of
∠
K
M
B
\angle KMB
∠
K
MB
, find
∠
M
L
C
\angle MLC
∠
M
L
C
.
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