Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 5Circular Measure

Solved on video in English · Form 5, Circular Measure · 7:17 video

The question

(a)

Diagram 4 shows two circles of radius 3 cm and 4 cm with centres A and B respectively, whose centres are 5 cm apart. The two circles intersect at C and D. The lines AC and BC are tangents to the circles centred at B and A respectively. [Use π = 3.142]

(a) Calculate the angle CAB, in radians.

(b)

Diagram 4 shows two circles of radius 3 cm (centre A) and 4 cm (centre B), centres 5 cm apart, intersecting at C and D, with AC and BC as tangents. [Use π = 3.142]

(b) Calculate the perimeter, in cm, of the whole diagram.

(c)

142]

(c) Calculate the area, in cm², of the whole diagram.

Kuala Lumpur Trial 2025 Add Maths Paper 2, Question 5: the question as drawn in Eduly's video7:17

Part (a)

Step 1

In triangle ACB the sides are AC = 3 cm, BC = 4 cm and AB = 5 cm.

3 more steps, each with the reason for it, in the full solution

Final answer

∠CAB = 0.9274 rad

Where students lose marks

Watch out: in the cosine rule, BC (opposite ∠CAB) is the side squared on its own. Give the answer in radians, not 53.13°.

Part (b)

5 more steps, each with the reason for it, in the full solution

Final answer

Perimeter = 33.27 cm

Where students lose marks

Watch out: the outer arc is the major arc, so use 2π − 2∠CAB, not 2∠CAB. Remember 2π = 6.284 here.

Part (c)

4 more steps, each with the reason for it, in the full solution

Final answer

Area = 71.91 cm²

Where students lose marks

Watch out: add the two major sectors AND both triangles ACB and ADB (12 cm² in total). Don't skip a triangle.

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