2022Q5(i)Tangents and Intersecting Chords

NumericalModerate2 marks

Two chords AB and CD of a circle intersect externally at E. If EC = 2 cm, EA = 3 cm and AB = 5 cm, find the length of CD.

Topic: Tangents / intersecting chords

Question diagram

Previous-year question practice database

Answer

Exam answer

CD = 10 cm

Explanation

By the secant theorem, EA × EB = EC × ED. EB = EA+AB = 8 cm. Thus 3×8 = 2×ED ⇒ ED=12; CD = ED−EC = 10 cm.

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