MathDB
Problems
Contests
International Contests
Caucasus Mathematical Olympiad
2020 Caucasus Mathematical Olympiad
7
7
Part of
2020 Caucasus Mathematical Olympiad
Problems
(1)
Parallel lines in a regular triangle
Source: 2020 Caucasus Mathematical Olympiad
3/16/2020
A regular triangle
A
B
C
ABC
A
BC
is given. Points
K
K
K
and
N
N
N
lie in the segment
A
B
AB
A
B
, a point
L
L
L
lies in the segment
A
C
AC
A
C
, and a point
M
M
M
lies in the segment
B
C
BC
BC
so that
C
L
=
A
K
CL=AK
C
L
=
A
K
,
C
M
=
B
N
CM=BN
CM
=
BN
,
M
L
=
K
N
ML=KN
M
L
=
K
N
. Prove that
K
L
∥
M
N
KL \parallel MN
K
L
∥
MN
.
geometry
Equilateral Triangle
easy problem