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JAMB Mathematics 2000 Question 30

Question 30

Circle Theorems

In the diagram above EFGH is a circle centre of O. FH is a diameter and GE is a chord which meets FH at right angle at the point N. If NH = 8cm and EG = 24cm, calculate FH.

Diagram for this question
  1. A.16cm
  2. B.20cm
  3. C.26cm
  4. D.32cm
Show the answer and explanation

Answer: C (26cm)

Explanation

The diameter bisects the chord, so EN = NG = 12 cm. By intersecting chords, FN × NH = EN × NG, so FN × 8 = 144 and FN = 18. FH = 18 + 8 = 26 cm.