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International Contests
Baltic Way
2015 Baltic Way
12
12
Part of
2015 Baltic Way
Problems
(1)
Circles and angles
Source: Baltic Way 2015
11/8/2015
A circle passes through vertex
B
B
B
of the triangle
A
B
C
ABC
A
BC
, intersects its sides
A
B
AB
A
B
and
B
C
BC
BC
at points
K
K
K
and
L
L
L
, respectively, and touches the side
A
C
AC
A
C
at its midpoint
M
M
M
. The point
N
N
N
on the arc
B
L
BL
B
L
(which does not contain
K
K
K
) is such that
∠
L
K
N
=
∠
A
C
B
\angle LKN = \angle ACB
∠
L
K
N
=
∠
A
CB
. Find
∠
B
A
C
\angle BAC
∠
B
A
C
given that the triangle
C
K
N
CKN
C
K
N
is equilateral.
geometry