2024Q9(i)Tangents and Intersecting Chords

NumericalModerate3 marks

The figure shows a circle of radius 9 cm with O as the centre. The diameter AB produced meets the tangent PQ at P. If PA = 24 cm, find the length of tangent PQ.

Topic: Tangents / intersecting chords

Question diagram

Previous-year question practice database

Answer

Exam answer

PQ = √1008 ≈ 31.75 cm.

Explanation

PB = PA+AB =24+18=42. Tangent-secant theorem: PQ²=PA·PB=24×42=1008.

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