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2022 CMIMC
2.3 1.2
2.3 1.2
Part of
2022 CMIMC
Problems
(1)
2022 Geo Div 1 P2 (Div 2 P3)
Source:
2/28/2022
Let
A
B
C
ABC
A
BC
be an acute triangle with
∠
A
B
C
=
6
0
∘
.
\angle ABC=60^{\circ}.
∠
A
BC
=
6
0
∘
.
Suppose points
D
D
D
and
E
E
E
are on lines
A
B
AB
A
B
and
C
B
,
CB,
CB
,
respectively, such that
C
D
B
CDB
C
D
B
and
A
E
B
AEB
A
EB
are equilateral triangles. Given that the positive difference between the perimeters of
C
D
B
CDB
C
D
B
and
A
E
B
AEB
A
EB
is
60
60
60
and
D
E
=
45
,
DE=45,
D
E
=
45
,
what is the value of
A
B
⋅
B
C
?
AB \cdot BC?
A
B
⋅
BC
?
Proposed by Kyle Lee
geometry