Cambridge International Mathematics

de f

g

XY and YZ are tangents

from point Y

hi

2 A circle is drawn and four tangents to it are constructed as

shown.

Deduce that AB+CD=BC+AD.

3 Find the radius of the circle which touches the three sides

of the triangle as shown.

4

5 Consider this figure:

a What can be deduced about:

i AbPO ii BbPO?

b Using¢APB, explain why 2 a+2b= 180 and

hence that a+b=90.

c What theorem have you proven?

6 In this question we prove thechords of a circletheorem.

a For the given figure join OA and OB and classify¢OAB.

b Apply the isosceles triangle theorem to triangle OAB.What

geometrical facts result?

O

82°

A

C

B

n°

x°

O

30°

Y X

a°

b°

X

Y

O

50°

70 °

Y

Z

X

a°

O b°

30 °

a°

40 °

b°

X

Y

O

A B

C

D

P

S

Q

R

3cm

4cm

O

C

A B

A circle is inscribed in a right angled triangle.

The radius of the circle is cm, and BC has

length cm.

Find the perimeter of the triangle ABC.

3

8

AB

P

O

a° b°

A

B

O

X

Circle geometry (Chapter 27) 551

m°

34°

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Y:\HAESE\IGCSE01\IG01_27\551IGCSE01_27.CDR Tuesday, 18 November 2008 11:02:12 AM PETER