CAIE IGCSE Mathematics Extended Circle Area Problems

Practise deriving a circle's radius from an inscribed square or regular polygon and comparing the circle's area with an internal shape.

Exam points

use the inscribed square's diagonal or regular polygon geometry to determine the circle radius
calculate circle area as πr² and retain an exact multiple of π when requested
divide an internal shape's area by πr² and multiply by 100 for a percentage comparison

[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

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E5.3.1 Carry out calculations involving the circumference and area of a circle. question 1