CAIE IGCSE Mathematics Extended E4.7 Circle Theorems I Topic Practice

CourseCourseConceptConceptDocumentDocument

Covered syllabus points

E4.7.1 Calculate unknown angles and give explanations using the following

Question 1

[Maximum number: 3]
NOT TO SCALE

NOT TO SCALE

The diagram shows a cyclic quadrilateral ABCD. BD and AC intersect at X.

Question (a)

(a)

Angle BAD=74∘B A D=74^{\circ} and angle BCA=34∘B C A=34^{\circ}.

Find

[ 3 ]

Question (i)

(i)

angle BDA

Angle B D A=

[ 1 ]

Question (ii)

(ii)

angle BCD

Angle B C D=

[ 1 ]

Question (iii)

(iii)

angle ABD.

Angle A B D=

[ 1 ]

Question 2

[Maximum number: 4]
Figure for Question 2 — CAIE IGCSE Mathematics Extended

\section*{NOT TO SCALE}
A, B and C lie on a circle centre O.
DE is a tangent to the circle at C.
Angle ABC=52∘A B C=52^{\circ} and angle BCE=65∘B C E=65^{\circ}.

Question (a)

(a)

Find the value of x.

Give a geometrical reason for your answer.
x= because

[ 2 ]

Question (b)

(b)

Find the value of y.

[ 2 ]

Question 3

[Maximum number: 4]
Figure for Question 3 — CAIE IGCSE Mathematics Extended

A, B, C and D are points on the circumference of a circle with centre O.
ED and EB are tangents to the circle.
AC is parallel to EB.
Angle AOD=44∘A O D=44^{\circ}.
Find the value of x.
x=

All question bank results loaded