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National and Regional Contests
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Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad (First Round)
7.
7.
Part of
2024 Korea Junior Math Olympiad (First Round)
Problems
(1)
Geometry, finding area.
Source: 2024 KJMO first round
10/26/2024
There are four collinear spots:
A
,
B
,
C
,
D
A,B,C,D
A
,
B
,
C
,
D
A
B
ˉ
=
B
C
ˉ
=
C
D
ˉ
4
=
5
\bar{AB}=\bar{BC}=\frac{\bar{CD}}{4}=\sqrt{5}
A
B
ˉ
=
BC
ˉ
=
4
C
D
ˉ
=
5
There are two circles; One which has
A
C
ˉ
\bar{AC}
A
C
ˉ
as a diameter, and the other having
B
D
ˉ
\bar{BD}
B
D
ˉ
as a diameter. Let's put
⊙
(
A
C
)
∩
⊙
(
B
D
)
=
E
,
F
\odot (AC) \cap \odot (BD) = E,F
⊙
(
A
C
)
∩
⊙
(
B
D
)
=
E
,
F
Let's put the area of
E
A
F
D
EAFD
E
A
F
D
S
S
S
Find
S
2
S^2
S
2
.
geometry