ECZ 2015 · GCE Paper 2 · Question 3 — Circle Theorems

Question from ECZ 2015 · GCE Paper 2 · Question 3

(a) In the diagram below, PAQ is a tangent to the circle at point A. AC bisects angle BCD. Angle ABC = 81° and angle PAB = 30°. Calculate;

(a(i)) angle ACB,[1]

Verified working — step 1

PA is a tangent and AB a chord.

(a(ii)) angle ADC,[1]

Verified working — step 1

ABCD is a cyclic quadrilateral.

(a(iii)) angle DAQ,[1]

Verified working — step 1

AC bisects angle BCD, so angle ACD = angle ACB = 30°.

(a(iv)) angle CAQ.[2]

Verified working — step 1

AQ is a tangent and AC a chord.

(b) Express 2b - 2 - 31 - 2b as a single fraction in its simplest form.[3]

Verified working — step 1

Note that 1 - 2b = -(2b - 1), so -31 - 2b becomes +32b - 1.

(c) Solve the inequation 4(1 - 2x) > 32.[2]

Verified working — step 1

Divide both sides by 4: 1 - 2x > 8.

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Original examination question © Examinations Council of Zambia. Worked solution and commentary © G12 Titan — not to be reproduced without permission.

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