Cambridge International Mathematics

Example 5 Self Tutor

Triangle ABC is isosceles with AB=AC. X and Y lie on AB and AC respectively such that XY is

parallel to BC. Prove that XYCB is a cyclic quadrilateral.

¢ABC is isosceles with AB=AC.

) ® 1 =® 2 fequal base anglesg

Since XYkBC, ® 1 =® 3 fequal corresp. anglesg

so, ® 2 =® 3

) XYCB is a cyclic quadrilateral

fexterior angle=opposite interior angleg

EXERCISE 27B.2

1 Is ABCD a cyclic quadrilateral? Give reasons for your answers.

abc

de f

2 ABCD is a trapezium in which AB is parallel to DC

and AD=BC.

Show that ABCD is a cyclic quadrilateral.

Hint: Draw BE parallel to AD, meeting DC at E.

3 AB and CD are parallel chords of a circle with centre

O. BC and AD meet at E.

Show that AEOC is a cyclic quadrilateral.

A

BC

X Y

az ax

ac

A D

BC

107°

73°

A

D

B

C

47°

47°

A

D

B

C

87°

87°

A

D

B

C

rectangle

A

E

D

B

C

80°

115°

50°

A

D

B

C

113°

113°

AB

D C

a°

AB

C D

E

O

560 Circle geometry (Chapter 27)

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_27\560IGCSE01_27.CDR Monday, 27 October 2008 2:40:54 PM PETER