CAIE IGCSE Mathematics Extended E4.7 Circle…ems I

Covered syllabus points

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

[Maximum number: 3]

NOT TO SCALE

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

(a)

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

Find

[ 3 ]

(i)

angle BDA

Angle B D A=

[ 1 ]

(ii)

angle BCD

Angle B C D=

[ 1 ]

(iii)

angle ABD.

Angle A B D=

[ 1 ]

[Maximum number: 2]

Figure for Question 2 — CAIE IGCSE Mathematics Extended

The diagram shows a shape made from a major sector AOB and triangles OBC and AOD. $O B=6 \mathrm{~cm}, B C=2 \mathrm{~cm}$ , obtuse angle $A O C=135^{\circ}$ and angle $B C O=90^{\circ}$ .

Show that angle $BOC=19.5^\circ$ , correct to 1 decimal place.

$\sin(BOC)=\frac26$ or better oe
19.47...

[Maximum number: 5]

Figure for Question 3 — CAIE IGCSE Mathematics Extended

Show that PQRS is a cyclic quadrilateral.

x+2 x-5+x+20+3 x-40=360
Accept equivalent equation

e.g. 7 x-25=360

7 x=360+5-20+40 or better
FT their equation, accept e.g. 7 x=385

x=55
55 and 125
or 105 and 75

B1dep

Dep on M1M1B1

Accept $55+3 \times 55-40=180$

or $2 \times 55-5+55+20=180$

If B0 scored, SC1 for 55, 75, 105 and 125

Opposite angles sum to 180 oe
[so PQRS is a cyclic quadrilateral ]
Dep on M1M1B1B1

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

Covered syllabus points

Question 1

Question (a)

Question (i)

Question (ii)

Question (iii)

Question 2

Question 3