Multiple choice

In a circle, AB and DC are the two chords. When AB and DC are produce. They meet at P. If PC = 5.6 cm, PB = 6.3 cm and AB = 7.7 cm, then the length of CD is?

  1. 8.35 cm

  2. 9 cm

  3. 10.15 cm

  4. 9.25 cm

Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two chords of a circle intersect externally (when produced), PA × PB = PC × PD. Given PC=5.6, PB=6.3, AB=7.7. PA = PB+AB = 6.3+7.7 = 14. Then 14 × 6.3 = 5.6 × PD → PD = 15.75. CD = PD-PC = 15.75-5.6 = 10.15 cm. The question has an image showing the intersecting chords.