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Turkey MO (2nd round)
2021 Turkey MO (2nd round)
3
3
Part of
2021 Turkey MO (2nd round)
Problems
(1)
6 points on a circle
Source: Turkey National Mathematical Olympiad 2021 P3
1/6/2022
A circle
Γ
\Gamma
Γ
is tangent to the side
B
C
BC
BC
of a triangle
A
B
C
ABC
A
BC
at
X
X
X
and tangent to the side
A
C
AC
A
C
at
Y
Y
Y
. A point
P
P
P
is taken on the side
A
B
AB
A
B
. Let
X
P
XP
XP
and
Y
P
YP
Y
P
intersect
Γ
\Gamma
Γ
at
K
K
K
and
L
L
L
for the second time,
A
K
AK
A
K
and
B
L
BL
B
L
intersect
Γ
\Gamma
Γ
at
R
R
R
and
S
S
S
for the second time. Prove that
X
R
XR
XR
and
Y
S
YS
Y
S
intersect on
A
B
AB
A
B
.
geometry