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Greece Junior Math Olympiad
2024 Greece Junior Math Olympiad
2
2
Part of
2024 Greece Junior Math Olympiad
Problems
(1)
junior perpenicularity, 2 circles related
Source: Greece Junior Math Olympiad 2024 p2
3/2/2024
Consider an acute triangle
A
B
C
ABC
A
BC
and it's circumcircle
ω
\omega
ω
. With center
A
A
A
, we construct a circle
γ
\gamma
γ
that intersects arc
A
B
AB
A
B
of circle
ω
\omega
ω
, that doesn't contain
C
C
C
, at point
D
D
D
and arc
A
C
AC
A
C
, that doesn't contain
B
B
B
, at point
E
E
E
. Suppose that the intersection point
K
K
K
of lines
B
E
BE
BE
and
C
D
CD
C
D
lies on circle
γ
\gamma
γ
. Prove that line
A
K
AK
A
K
is perpendicular on line
B
C
BC
BC
.
geometry
perpendicular