Cambridge International Mathematics

A

B

C

D

a°

O b°

2 Copy and complete:

Obtuse DbOB=:::::: f::::::g

Likewise, reflex DbOB=:::::: f:::::::g

) ::::::+::::::= 360o fangles at a pointg

) ®+ ̄=::::::

Thus, the opposite angles of a ...... are ......

3 The circle inscribed in triangle PQR has radius of

length 3 cm.

PQ has length 7 cm.

Find the perimeter of triangle PQR.

4 In triangle PQR, PQ =PR. A circle is drawn with

diameter PQ, and the circle cuts QR at S.

Show that S is the midpoint of QR.

5 In this question we prove theangle between a tangent and a

chordtheorem.

a We draw diameter AX and join CX.

Find the size of: i TAXb ii ACXb

b Now let TACb =®. Find, in terms of®:

i CAXb ii CbXA iii CBAb

Give reasons for your answers.

6 Using the result of 5 , find:

a BbCX and CBXb

b ®+ ̄+°

7

P

QR

P

R

S

Q

O

T

A

B

C

X

a

O

a

b

A g

B

C

X

P

Q

T

R

S

V PV is a tangent to the circle and QT is parallel to PV.

Use the result of to prove that QRST is a cyclic

quadrilateral.

5

Circle geometry (Chapter 27) 563

IGCSE01

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Y:\HAESE\IGCSE01\IG01_27\563IGCSE01_27.CDR Tuesday, 28 October 2008 10:00:05 AM PETER