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 it.

Possible approach

Ask learners to write down the lengths in the diagram in terms of the radii of the three circles. Let them introduce their own notation.

Key question

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?

Possible extension

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.