### Why do this problem?

In

this
problem, the dynamc geometry applet provides an opportunity for
experimenting and making conjectures. The proof can be done
entirely by similar triangles but there are several possible
methods. A useful problem-solving skill to apply is to simplify the
image and another is the magic of the key construction line that
opens up new possibiliites.

### Possible approach

Give the class time to experiment and make their own
conjectures.

Make a list and chose one as a focus. The
'obvious' one is that the two chords are equal but they might, for
example, notice that they are perpendicular to the line joining the
centres.

Having identified a conjecture of interest, ask learners to
write on separate cards statements about the figure that they know
are true or think might be true (and distinguish between
them).

In groups look at the the statements they have and try to
arrange them into those they think are useful and those not and
those aperson can justufy and those they
cannot.

Now try to order or arrange them further discussing the
possible use they might be or insights they might offer.

Can they come up with any further statements?

Share ideas ready to put together a more formal
proof. Why not emphasisethe messiness of
getting to a stage where enough is known, and a direction has
emerged, before formalising a proof.

### Key questions

- Can you see any similar triangles?
- Can you see symmetry in the diagram?
- Is there a line you could draw that might give us a new
insight?
- Do we need all the diagram?

### Possible extension

Try the problem

Belt
### Possible support

Encourage the learners to draw the dynamic diagram for themselves
using

Geogebra.