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International Zhautykov Olympiad
2018 International Zhautykov Olympiad
2
IZHO 2018 P2(geometry)
IZHO 2018 P2(geometry)
Source: izho2018
February 14, 2018
geometry
incenter
geometry unsolved
Problem Statement
Let
N
,
K
,
L
N,K,L
N
,
K
,
L
be points on
A
B
,
B
C
,
C
A
AB,BC,CA
A
B
,
BC
,
C
A
such that
C
N
CN
CN
bisector of angle
∠
A
C
B
\angle ACB
∠
A
CB
and
A
L
=
B
K
AL=BK
A
L
=
B
K
.Let
B
L
∩
A
K
=
P
BL\cap AK=P
B
L
∩
A
K
=
P
.If
I
,
J
I,J
I
,
J
be incenters of triangles
△
B
P
K
\triangle BPK
△
BP
K
and
△
A
L
P
\triangle ALP
△
A
L
P
and
I
J
∩
C
N
=
Q
IJ\cap CN=Q
I
J
∩
CN
=
Q
prove that
I
Q
=
J
P
IQ=JP
I
Q
=
J
P
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