Cambridge International Mathematics

gh i

3 C is the point of contact of tangent CT.

Findx, giving reasons for your answer.

Hint: Draw diameter CD and join DB.

4 In this question we prove theangle at the centretheorem.

a Explain why¢s OAP and OBP are isosceles.

b Find the measure of the following angles in terms ofa

andb:

i AbPO ii BbPO iii AOXb

iv BOXb v AbPB vi AOBb

c What can be deduced frombvandbvi?

5 In this question we prove theangles in the same segmenttheorem.

a Using the results of question 4 , find the size of AOB inb

terms of®.

b Find the size of ACB in terms ofb ®.

c State the relationship between ADB and Ab CB.b

6 Challenge:

In the figure alongside, AC=BC, and the

tangents at A and C meet at D.

Show that ®+ ̄=90:

96°

x°

54° 20°

O x° 65°

x°

O

T

A

B

C

40°

x°

A

B

C

D

a

O

A

B

P

X

a

b

O

O

D

C

B

A

a°

b°

Circle geometry (Chapter 27) 555

IGCSE01

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Y:\HAESE\IGCSE01\IG01_27\555IGCSE01_27.CDR Tuesday, 28 October 2008 9:43:25 AM PETER