Circle geometry

27

Contents:

A Circle theorems [4.7]

B Cyclic quadrilaterals [4.7]

Opening problem

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The towns of Arden, Barne, Cowley and Dirnham are

all the same distance from the town of Oakden. Both

Barne and Dirnham are equidistant from Arden and

Cowley.

Can you prove that Barne, Oakden and Dirnham are

collinear?

Before we can talk about the properties and theorems of circles, we need to learn the appropriate language

for describing them.

² Acircleis the set of all points which are equidistant from a fixed

point called thecentre.

² The circumference is the distance around the entire circle

boundary.

A CIRCLE THEOREMS [4.7]

Arden

Barne

Cowley

Dirnham

Oakden

centre

circle

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Y:\HAESE\IGCSE01\IG01_27\547IGCSE01_27.CDR Monday, 27 October 2008 2:39:49 PM PETER