MathDB

Austrian-Polish Mathematical Olympiad 1992

Source:

April 28, 2011

ratiogeometry

Problem Statement

Given a circle

G

with center

O

and radius

r

. Let

AB

be a fixed diameter of

K

. Let

P

be a fixed point of segment

Q

. Denote by

t

the line tangent to at

A

. For any chord

CD

(other than

AB

) passing through

K

. Let

P

and

Q

be the points of intersection of lines

BC

and

BD

with

t

. Prove that the product

AP\cdot AQ

remains costant as the chord

CD

varies.

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