Cambridge International Mathematics

² Anarcof a circle is any continuous part of the circle.

² Achordof a circle is a line segment joining any two points on

the circle.

² Asemi-circleis a half of a circle.

² Adiameterof a circle is any chord passing through its centre.

² Aradiusof a circle is any line segment joining its centre to any

point on the circle.

² Atangentto a circle is any line which touches the circle in

exactly one point.

Discovery 1 Properties of circles

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This discovery is best attempted using thecomputer packageon the CD.

However, you can also use a compass, ruler and protractor.

Part 1: The angle in a semi-circle

What to do:

1 Draw a circle and construct a diameter. Label it as shown.

2 Mark any point P not at A or B on the circle.

Draw AP and PB.

3 Measure angle APB.

4 Repeat for different positions of P and for different circles.

What do you notice?

5 Copy and complete: The angle in a semi-circle is ......

Part 2: Chords of a circle theorem

What to do:

1 Draw a circle with centre C. Construct any chord AB.

2 Construct the perpendicular from C to AB which cuts the

chord at M.

3 Measure the lengths of AM and BM. What do you notice?

4 Repeat the procedure above with another circle and chord.

5 Copy and complete:

The perpendicular from the centre of a circle to a chord

......

arc

chord

diameter

radius

tangent

point of contact

GEOMETRY

PACKAGE

GEOMETRY

PACKAGE

A B

P

O

A

B

C

548 Circle geometry (Chapter 27)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_27\548IGCSE01_27.CDR Monday, 27 October 2008 2:40:22 PM PETER