Why do this problem?
It involves learners in visualisation and working with
dynamic images and in conjecturing and proving. They
have to select the mathematical information, methods
and tools to use.
Possible approach
You might use this problem in connection with work on
circle theorems or later as an application and revision
of previous work. You might accept the statement that a
line joining the centres of two circles is
perpendicular to the common chord or you might ask
learners to prove this.