EduNinja

[Maximum number: 3]

NOT TO SCALE

A, B and C are points on the circle, centre O.
DE is a tangent to the circle at C.
AC=10 cm, AB=9.5 cm and BC=7.7 cm.

(a)

Find

[ 3 ]

(i)

angle AOC

[ 1 ]

(ii)

angle ACO

\text { Angle } A C O=

[ 1 ]

19.8
FT $(180-\text{their (b)(i)})\div2$

(iii)

angle ACD.

\text { Angle } A C D=

[ 1 ]

70.2
FT $90-\text{their (b)(ii)}$

[Maximum number: 8]

(a)

Figure for Question (a) — CAIE IGCSE Mathematics Extended

\section*{NOT TO SCALE}
A, B, C and D are points on a circle.
PQ is the tangent to the circle at A.
BMND is a straight line.
Angle $A C D=49^{\circ}$ , angle $A M B=105^{\circ}$ and angle $P A B=45^{\circ}$ .

[ 5 ]

(i)

Find angle BAM.

Angle B A M=

[ 2 ]

26
B1 for $\angle ABD=49^\circ$

(ii)

(a) Find angle BAD.

Angle B A D=

(b)

Give a geometrical reason why BD is not the diameter of the circle.

[ 3 ]

(a) 86
B1 for $\angle QAD=49^\circ$ or for $\angle BDA=45^\circ$ or for $\angle BCA=45^\circ$

(b) Angle in a semicircle $=90^\circ$

(b)

Figure for Question (b) — CAIE IGCSE Mathematics Extended

A, B, C and D are points on a circle, centre O.
TA and TC are tangents to the circle.
$O A=6.75 \mathrm{~cm}$ and $O T=11.5 \mathrm{~cm}$ .

[ 3 ]

(i)

Show that angle $A O C=108.12^{\circ}$ , correct to 2 decimal places.

[ 3 ]

$[2\times]\cos^{-1}\left(\frac{6.75}{11.5}\right)$ oe
M1 for $\cos(\ldots)=\frac{6.75}{11.5}$ oe
$108.117\ldots$

[Maximum number: 5]

(a)

NOT TO SCALE

Points R and S lie on a circle with diameter PQ.
RQ is parallel to PS.
Angle $R P Q=58^{\circ}$ .
Find the value of x, giving a geometrical reason for each stage of your working.

x=

[ 3 ]

(b)

Points A, B and C lie on a circle, centre O. Angle $A O C=142^{\circ}$ .

Find the value of y.

y=

[ 2 ]

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

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 2

Question (a)

Question (i)

Question (ii)

Question (b)

Question (i)

Question 3

Question (a)

Question (b)