Cambridge International Mathematics

Name of theorem Statement Diagram

Radius-tangent The tangent to a circle is

perpendicular to the radius

at the point of contact.

ObAT=90o

Tangents from an

external point

Tangents from an external

point are equal in length.

AP=BP

Two usefulconversesare:

² If line segment AB subtends a right angle at C then the circle

through A, B and C has diameter AB.

²

Example 1 Self Tutor

Findx, giving brief reasons for

your answer.

ABC measuresb 90 o fangle in a semi-circleg

) (x+ 10) + 3x+ 90 = 180 fangles in a triangleg

) 4 x+ 100 = 180

) 4 x=80

) x=20

EXERCISE 27A.1

1 Find the value of any unknowns, giving brief reasons for your answers:

abc

A

T

O

A

B

O P

A C

B

()x¡+¡10° 3 x°

A

B

C

The perpendicular bisector of a chord of a

circle passes through its centre.

53° x°

O x° () 2 x°

O

() 2 x°

() 3 x°

O

550 Circle geometry (Chapter 27)

IGCSE01

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Y:\HAESE\IGCSE01\IG01_27\550IGCSE01_27.CDR Monday, 27 October 2008 2:40:27 PM PETER