Multiple choice

Two chords AB and CD of a circle are produced to intersect each other at a point P outside the circle. If AB = 7 cm, BP = 4.2 cm and PD = 2.8 cm, then the length of CD is:

  1. 12 cm

  2. 14.6 cm

  3. 15.8 cm

  4. 14 cm

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

When two chords AB and CD of a circle intersect outside at point P, by the power of a point theorem: PA × PB = PC × PD. Given AB = 7 cm and BP = 4.2 cm, we have PA = AB + BP = 7 + 4.2 = 11.2 cm. So PC × PD = PA × PB = 11.2 × 4.2 = 47.04. With PD = 2.8 cm, PC = 47.04 ÷ 2.8 = 16.8 cm. Therefore CD = PC - PD = 16.8 - 2.8 = 14 cm.