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9
SMT 2022 Geometry #9
SMT 2022 Geometry #9
Source:
April 1, 2023
Problem Statement
The bisector of
∠
B
A
C
\angle BAC
∠
B
A
C
in
△
A
B
C
\triangle ABC
△
A
BC
intersects
B
C
BC
BC
in point
L
L
L
. The external bisector of
∠
A
C
B
\angle ACB
∠
A
CB
intersects
B
A
→
\overrightarrow{BA}
B
A
in point
K
K
K
. If the length of
A
K
AK
A
K
is equal to the perimeter of
△
A
C
L
\triangle ACL
△
A
C
L
,
L
B
=
1
LB=1
L
B
=
1
, and
∠
A
B
C
=
3
6
∘
\angle ABC=36^\circ
∠
A
BC
=
3
6
∘
, find the length of
A
C
AC
A
C
.
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