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National and Regional Contests
Mexico Contests
Mexico National Olympiad
2004 Mexico National Olympiad
3
3
Part of
2004 Mexico National Olympiad
Problems
(1)
Mexican equal segments II
Source: Mexican Mathematical Olympiad 2004 OMM P3
7/31/2018
Let
Z
Z
Z
and
Y
Y
Y
be the tangency points of the incircle of the triangle
A
B
C
ABC
A
BC
with the sides
A
B
AB
A
B
and
C
A
CA
C
A
, respectively. The parallel line to
Y
Z
Y Z
Y
Z
through the midpoint
M
M
M
of
B
C
BC
BC
, meets
C
A
CA
C
A
in
N
N
N
. Let
L
L
L
be the point in
C
A
CA
C
A
such that
N
L
=
A
B
NL = AB
N
L
=
A
B
(and
L
L
L
on the same side of
N
N
N
than
A
A
A
). The line
M
L
ML
M
L
meets
A
B
AB
A
B
in
K
K
K
. Prove that
K
A
=
N
C
KA = NC
K
A
=
NC
.
geometry
equal segments