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Contests
National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2024 Korea Junior Math Olympiad
5
5
Part of
2024 Korea Junior Math Olympiad
Problems
(1)
ANALYTIC GEO?
Source: 2024 KJMO P5
11/9/2024
A
B
C
ABC
A
BC
is a right triangle with
∠
C
\angle C
∠
C
the right angle.
X
X
X
is some point inside
A
B
C
ABC
A
BC
satisfying
C
A
=
A
X
CA=AX
C
A
=
A
X
. Let
D
D
D
be the feet of altitude from
C
C
C
to
A
B
AB
A
B
, and
Y
(
≠
X
)
Y(\neq X)
Y
(
=
X
)
the point of intersection of
D
X
DX
D
X
and the circumcircle of
A
B
X
ABX
A
BX
. Prove that
A
X
=
A
Y
AX=AY
A
X
=
A
Y
.
geometry
circumcircle