EduNinja

[Maximum number: 4]

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.

Calculate the area of triangle ABC as a percentage of the area of the circle.

38.8 or 38.9 or 38.78 to 38.85
M3 for $\frac{0.5\times9.5\times7.7\times\sin70.2}{\pi(\text{their (c)})^2}\times100$ oe
or lower method marks as in markscheme

[Maximum number: 3]

NOT TO SCALE

The diagram shows a sector of a circle with radius 8 cm and angle $75^{\circ}$ .
Find the perimeter of the sector.
cm

26.5 or 26.47...
B2 for 10.5 or 10.47... or $\frac{10\pi}{3}$
OR M2 for $8+8+\frac{75}{360}\times2\pi\times8$
or M1 for $\frac{75}{360}\times2\pi\times8$

[Maximum number: 3]

ABCDEFGH is a regular octagon with sides of length 6 cm. The diagram shows part of the octagon.
O is the centre of the octagon and M is the midpoint of AB.

Figure for Question 3 — CAIE IGCSE Mathematics Extended

NOT TO SCALE

Find the area of the circle that passes through the vertices of the octagon.
$\mathrm{cm}^{2}$

193 or 193.0 to 193.1
M2 for $\pi\left(\frac3{\cos67.5^\circ}\right)^2$ oe
or M1 for $\frac3r=\cos67.5^\circ$ or $\frac{\sin45^\circ}{6}=\frac{\sin67.5^\circ}{r}$

CAIE IGCSE Mathematics Extended E5.3 Circles Arcs and Sectors Topic Practice

Question 1

Question 2

Question 3