Why do this
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.
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.
What stays invariant as the diagram changes?
What is changing?
What do you notice about the quadrilateral PQRS as the diagram
What other questions can we ask about this figure?
What happens if one of the vertices A, B, C or D moves on top of
another one or on top of the
point X (degenerate cases)?
What happens if ABCD is not convex?
Try the problems:
Draw the dynamic diagram for yourself. Geogebra
is very easy to use and it