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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad (First Round)
20.
20.
Part of
2024 Korea Junior Math Olympiad (First Round)
Problems
(1)
Easy Geometry
Source: 2024 KJMO first round
10/27/2024
There is a
△
A
B
C
\triangle ABC
△
A
BC
which
∠
C
=
90
\angle C=90
∠
C
=
90
, and
A
B
ˉ
=
36
\bar{AB}=36
A
B
ˉ
=
36
On the circumcircle of
△
A
B
C
\triangle ABC
△
A
BC
, there is \overarc{BC} which does not include point
A
A
A
. D is on \overarc{BC}. It satisfies
2
×
∠
C
A
D
=
∠
B
A
D
2\times\angle CAD = \angle BAD
2
×
∠
C
A
D
=
∠
B
A
D
E
:
A
D
ˉ
∩
B
C
ˉ
E: \bar{AD}\cap\bar{BC}
E
:
A
D
ˉ
∩
BC
ˉ
A
E
ˉ
=
20
\bar{AE}=20
A
E
ˉ
=
20
Find
B
D
ˉ
2
\bar{BD}^2
B
D
ˉ
2
geometry
circumcircle