Why do this problem?
Triangles in Circles
. It leads to the theorem about right-angles in
Teachers may find the article Angle
Measurement: An Opportunity For Equity
to be of interest.
If students are going to be working at individual computers,
demonstrate how the geoboard works - clicking on a coloured rubber
band, dragging it onto a peg and then "stretching" it out onto two
more pegs to make a triangle.
If students will be working on paper ask them to draw right-angled
triangles on their 9-peg
How many different triangles can they find?
How do they know they are right-angled?
What is special about the right-angled triangles?
Draw together conjectures which might mention the number of dots on
the circle and the need to be able to join two points to form a
diameter. Challenge students to justify these conjectures with
convincing arguments. Eventually link this to the work on Subtended
What do we know already that might be useful here?
What is the relationship between the angle at the centre and the
angle at the circumference?
What are the implications of our findings for circles in general
Ask students to prove the general case.
Students may need to spend more time convincing themselves when it
is possible to make right-angled triangles. Here
is a sheet with 10-peg,
12-peg and 16-peg circles to support them in investigating other