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5.
2022 Polish Junior Math Olympiad First Round P5
2022 Polish Junior Math Olympiad First Round P5
Source:
May 21, 2023
geometry
Problem Statement
Points
K
K
K
,
L
L
L
,
M
M
M
lie on the sides
B
C
BC
BC
,
C
A
CA
C
A
,
A
B
AB
A
B
of equilateral triangle
A
B
C
ABC
A
BC
respectively, and satisfy the conditions
K
M
=
L
M
KM=LM
K
M
=
L
M
,
∠
K
M
L
=
9
0
∘
\angle KML=90^\circ
∠
K
M
L
=
9
0
∘
, and
A
M
=
B
K
AM=BK
A
M
=
B
K
. Prove that
∠
C
K
L
=
9
0
∘
\angle CKL=90^\circ
∠
C
K
L
=
9
0
∘
.
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