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XP/YQ is independent of m

Source: Baltic Way 2017 Problem 12

November 11, 2017

geometryratio

Problem Statement

Line

\ell

touches circle

S_1

in the point

X

and circle

S_2

in the point

Y

. We draw a line

m

which is parallel to

\ell

and intersects

S_1

in a point

P

and

S_2

in a point

Q

. Prove that the ratio

XP/YQ

does not depend on the choice of

m

.

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