Cambridge International Mathematics

4 A circle has centre O. The tangents to the circle from an external point P meet the circle at points A

and B. Show that PAOB is a cyclic quadrilateral.

5 Triangle ABC has its vertices on a circle. P, Q and R are any points on arcs AB, BC and AC respectively.

Prove that AbRC+BQCb +AbPB= 360o:

6 Two circles intersect at X and Y. A line segment

AB is drawn through X to cut one circle at A

and the other at B. Another line segment CD

is drawn through Y to cut one circle at C and

the other at D, with A and C being on the same

circle. Show that AC is parallel to BD.

Review set 27A

#endboxedheading

1 Find the value ofa, giving reasons:

abc

de f

gh i

2 Copy and complete:

Triangle OAC is isosceles fas AO=......g

) AbCO=...... f.......g

Likewise, triangle BOC is ......

) BCOb =...... f......g

Thus the angles of triangle ABC measureao,boand ......

) 2 a+2b=:::::: f......g

) a+b=::::::

and so AbCB =......

A X

B

D

C Y

102°

41°

a°

28° a°

O

240°

80°

a°

OO

( \+30)a °

110° 63°

a°

3°a

a°

a°

36°

O

a°

O

97°

a°

AB

C

O

a° b°

Circle geometry (Chapter 27) 561

IGCSE01

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Y:\HAESE\IGCSE01\IG01_27\561IGCSE01_27.CDR Monday, 27 October 2008 2:40:56 PM PETER