Cambridge International Mathematics

A circle can always be drawn through any three points that are not

collinear.

To find the circle’s centre we draw the perpendicular bisectors of

the lines joining two pairs of points.

Using the chords of a circle theorem, the centre is at the intersection

of these two lines.

If a circle can be drawn through four points we say that the points areconcyclic.

If any four points on a circle are

joined to form a convex quadrilateral then

the quadrilateral is said to be a cyclic

quadrilateral.

CYCLIC QUADRILATERAL THEOREMS

Name of theorem Statement Diagram

Opposite angles of a

cyclic quadrilateral

The opposite angles of a cyclic

quadrilateral are supplementary,

or add to 180 o.

®+ ̄= 180

μ+Á= 180

Exterior angle of a

cyclic quadrilateral

The exterior angle of a cyclic

quadrilateral is equal to the

opposite interior angle.

μ 1 =μ 2

B CYCLIC QUADRILATERALS [4.7]

centre

P 1

P 2

P 3

4 point Pth 4

P 1

P 2

P 3

P 4

However, a circle may or may not be

drawn through any four points in a plane.

For example, consider the sets of points

opposite:

b°

a°

q°

f°

q

q

556 Circle geometry (Chapter 27)

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Y:\HAESE\IGCSE01\IG01_27\556IGCSE01_27.CDR Monday, 27 October 2008 2:40:43 PM PETER