Stage: 3 and 4 Challenge Level:
Why do this problem?
The problem gives an opportunity for learners to make a conjecture
and then to test whether their conjecture holds, and totry to prove
Ask learners to write down the lengths in the diagram in terms of
the radii of the three circles. Let them introduce their own
At a point of contact between two circles, the circles have a
common tangent. What can you say about the lines from the centres
of the two circles to the point of contact?
Download a free copy of the program Geogebra and let learners use
it to experiment and to draw their own dynamic mathematics diagrams
including the diagram from this question.