### Why do this problem :

This superficially fixed problem is an excellent way to draw
students into the discovery of a general result. There are likely
to be a range of possible routes to solution giving ample
opportunity for discussion of other people's approaches and the
elegance and efficiency of approaches.

### Possible approach :

It seems at first as though there's not enough information to
fix the angle whose size we are asked to establish - parts of the
construction seem to have a lot of freedom to wander.

But as this situation is explored more it becomes apparent that
the angle of interest maintains its size wherever the unconstrained
parts of the diagram happen to rest.

This freedom to wander may be clear to the group almost
immediately but if it is not, ask the students to reproduce the
figure using the given values. This should help them appreciate
what hasn't been specified, and lead them to question whether it is
necessary for these to be specified.

Now they have something to explore.

Dynamic Geometry may help with enquiry, but isn't essential. Two
drawings of the figure with measurements of the angle should be
enough to suggest a possible general result which can then be
reasoned over.

In conjunction with the problem presented the following
connected result can be included : allow one fixed length chord to
move around a given circle, relative to a second chord of some
other fixed length. Joining the end of each chord to the opposite
end of the other will produce two diagonal lines which, it turns
out, intersect at the same angle regardless of the relative
position of the chords.

### Key questions :

- Can anyone see how we could know the size of the missing angle
- or any ideas how we might try to find it ?

- Any thoughts at all about the problem ?

- Can you describe how to draw this diagram ? What do you do
first ? Then what ?

### Possible extension :

Trapezium
Four
### Possible support :

This is an opportunity for plenty of drawing and measuring of
angles associated with circles. All the standard angles in circles
results can be acquired through discover and the justification for
each as it emerges will be an important exercise in geometric
reasoning.