Multiple choice

AB and CD are two chords of a circle which intersect each other at a point O inside the circle. It is given that, AB = 10 cm, CO= 1.5 cm and DO = 12.5 cm. What is the ratio between the larger and smaller among AO and BO?

  1. $3 : 2$
  2. $4 : 1$
  3. $7 : 3$
  4. $3 : 1$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When two chords intersect inside a circle, the products of their segments are equal: AO × BO = CO × DO. Given CO = 1.5 cm and DO = 12.5 cm, their product is 18.75. Since AB = 10 cm, AO + BO = 10. Solving x(10-x) = 18.75 gives x = 7.5 and 2.5, making the ratio 7.5:2.5 = 3:1. Option D is correct.

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