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International Contests
Baltic Way
2017 Baltic Way
12
12
Part of
2017 Baltic Way
Problems
(1)
XP/YQ is independent of m
Source: Baltic Way 2017 Problem 12
11/11/2017
Line
ℓ
\ell
ℓ
touches circle
S
1
S_1
S
1
in the point
X
X
X
and circle
S
2
S_2
S
2
in the point
Y
Y
Y
. We draw a line
m
m
m
which is parallel to
ℓ
\ell
ℓ
and intersects
S
1
S_1
S
1
in a point
P
P
P
and
S
2
S_2
S
2
in a point
Q
Q
Q
. Prove that the ratio
X
P
/
Y
Q
XP/YQ
XP
/
Y
Q
does not depend on the choice of
m
m
m
.
geometry
ratio