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Lusophon Mathematical Olympiad
2015 Lusophon Mathematical Olympiad
1
1
Part of
2015 Lusophon Mathematical Olympiad
Problems
(1)
Angle(s) Bisector(s)
Source: Training for IMO/Cono sur
9/15/2017
In a triangle
A
B
C
,
L
ABC, L
A
BC
,
L
and
K
K
K
are the points of intersections of the angle bisectors of
∠
A
B
C
\angle ABC
∠
A
BC
and
∠
B
A
C
\angle BAC
∠
B
A
C
with the segments
A
C
AC
A
C
and
B
C
BC
BC
, respectively. The segment
K
L
KL
K
L
is angle bisector of
∠
A
K
C
\angle AKC
∠
A
K
C
, determine
∠
B
A
C
\angle BAC
∠
B
A
C
.
geometry
angle bisector