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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2001 Korea Junior Math Olympiad
3
3
Part of
2001 Korea Junior Math Olympiad
Problems
(1)
2001 KJMO P3
Source: 2001 KJMO P3
6/29/2024
A
,
B
A, B
A
,
B
are points on circle
O
O
O
satisfying
∠
A
O
B
<
12
0
∘
\angle AOB < 120^{\circ}
∠
A
OB
<
12
0
∘
.
C
C
C
is a point on the tangent line of
O
O
O
passing through
A
A
A
satisfying
A
B
=
A
C
AB=AC
A
B
=
A
C
and
∠
B
A
C
<
9
0
∘
\angle BAC < 90^{\circ}
∠
B
A
C
<
9
0
∘
.
D
D
D
is the intersection of
O
O
O
and
B
C
BC
BC
not
B
B
B
, and
I
I
I
is the incenter of
A
B
D
ABD
A
B
D
. Prove that
A
E
=
A
C
AE=AC
A
E
=
A
C
where
E
E
E
is the intersection of
C
I
CI
C
I
and
A
D
AD
A
D
.
geometry
incenter