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Turkey Contests
Turkey Junior National Olympiad
2023 Turkey Junior National Olympiad
2
2
Part of
2023 Turkey Junior National Olympiad
Problems
(1)
Incenters on an inscribed quadrilateral
Source: 2023 Turkey Junior National Olympiad P2
12/22/2023
Let
A
B
C
D
ABCD
A
BC
D
be an inscribed quadrilateral. Let the incenters of
B
A
D
BAD
B
A
D
and
C
A
D
CAD
C
A
D
be
I
I
I
and
J
J
J
respectively. Let the intersection point of the line that passes through
I
I
I
and perpendicular to
B
D
BD
B
D
and the line that passes through
J
J
J
and perpendicular to
A
C
AC
A
C
be
K
K
K
. Prove that
K
I
=
K
J
KI=KJ
K
I
=
K
J
geometry
incenter