Cambridge International Mathematics

660 Multi-Topic Questions (Chapter 33)

b

c Writehin terms of¼andt.

d If h=1and the arc length, AB, is 1 m, calculate

i angle AOB ii the area of the sector AOB.

28

In the triangle ABC, AB=xcm. The side AC is 3 cm shorter than AB and the side BC is 5 cm

shorter than AB.

aiShow that the perimeter of the triangle,pcm, is given by p=3x¡ 8.

ii The perimeter is 212 times the length of AB. Find the length of AB.

iii

biIf, instead, the triangle ABC is right angled, show that x^2 ¡ 16 x+34=0.

ii Solve the equation x^2 ¡ 16 x+34=0giving your answers correct to 2 decimal places.

iii Hence find the lengths of the sides of the right-angled triangle.

29 Nov 1995, Paper 4

O is the centre of the circle. Angle BOD= 132o.

The chords AD and BC meet at P.

aiCalculate angles BAD and BCD.

ii Explain why triangles ABP and CDP are similar.

iii AP=6cm, PD=8cm, CP=3cm and

AB=17: 5 cm.

Calculate the lengths of PB and CD.

iv If the area of triangle ABP isncm^2 , write down,

in terms ofn, the area of triangle CPD.

biThe tangents at B and D meet at T. Calculate angle BTD.

ii Use OB=9: 5 cm to calculate the diameter of the circle which passes through O, B, T and

D, giving your answer to the nearest centimetre.

30

a ABCDE is a semicircle of diameter 10 centimetres.

AC=CE and angle ACE=90o. Calculate

i the area of the semicircle

ii the area of triangle ACE

iii

b PQ and QR are tangents to a semicircle with

centre O and diameter 10 centimetres. POR is a

straight line, PQ=QR and angle PQR=90o.

Calculate the area of triangle PQR.

A

C

P

O 132°

B

D

AE

B D

C

O

10 cm

10 cm

PRO

Q

PRINTABLE QUESTIONS

Find the length of a pendulum which takes 1 second to move from A to B.

Click on the icon to obtain 24 more multi-topic questions.

Given that angle ACB=83: 2 oand caseiiapplies, calculate the smallest angle of the triangle,

giving your answer correct to the nearest degree.

Adapted from Nov 1995, Paper 4

Adapted from Nov 1998, Paper 4

the area of the shaded segment ABC.

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Y:\HAESE\IGCSE01\IG01_33\660IGCSE01_33.CDR Friday, 14 November 2008 10:38:06 AM PETER