MathDB

Let

AB

be a diameter of a circle

S

, and let

L

be the tangent at

A

. Furthermore, let

c

be a fixed, positive real, and consider all pairs of points

X

and

Y

lying on

L

, on opposite sides of

A

, such that |AX|\cdot |AY| \equal{} c. The lines

BX

and

BY

intersect

S

at points

P

and

Q

, respectively. Show that all the lines

PQ

pass through a common point.

Problem Statement