A is a fixed pt on a given circle; AP , AQ are variable chords such that AP.AQ is constant. Prove that PQ touches a fixed circle, centre A
unfortunately I can't give you a proof of this statement.
I've sketched a few different situations and obviously the statement seems to be true. With the drawing (see attachment) I choose:
R = 6 cm
. Then I got the radius of the circle with centre A is 4 cm long. Probably there exists the "rule"(?):