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# Right Angles

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Age 11 to 14

Challenge Level

*Right Angles printable sheet
Link to a collection of printable sheets of circle templates.*

Can you make a right-angled triangle on this peg-board by joining up three points round the edge?

Can you work systematically to prove this?

Now try changing the number of points round the edge.

Can you do it now?

Can you show by calculation that the angle is a right angle?

What do you notice about the side of the triangle opposite the right angle?

Try this with other numbers of points round the edge.

When is it possible to make a right-angled triangle?

In this interactivity, the points are equally spaced around a circle. Imagine that they are not.

Can you explain the conditions which will give a right-angled triangle?

Can you prove this?

Many thanks to Geoff Faux who introduced us to the merits of the 9 pin circular geo-board.

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

Two circles are enclosed by a rectangle 12 units by x units. The distance between the centres of the two circles is x/3 units. How big is x?

This gives a short summary of the properties and theorems of cyclic quadrilaterals and links to some practical examples to be found elsewhere on the site.