MathDB

fixed circle, fixed diameter, fixed point lead to constant product AP\cdot AQ

Source: Austrian-Polish 1992

May 24, 2019

geometryFixed pointfixedcircleProduct

Problem Statement

Given a circle

k

with center

M

and radius

r

, let

AB

be a fixed diameter of

k

and let

K

be a fixed point on the segment

AM

. Denote by

t

the tangent of

k

A

. For any chord

CD

through

K

other than

AB

, denote by

P

and Q the intersection points of

BC

and

BD

with

t

, respectively. Prove that

AP\cdot AQ

does not depend on

CD