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Two chords AB and CD of a circle intersect externally at a point P. If PC = 15 cm, CD = 7 cm and AP = 12 cm, then AB is

  1. 2 cm

  2. 4 cm

  3. 6 cm

  4. none of these

Two chords AB and CD of a circle intersect externally at a point P. If PC = 15 cm, CD = 7 cm and AP = 12 cm, then AB is (a) 2 cm (b) 4 cm (c) 6 cm (d) none of these. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Circles

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Answer

We know that if two chords of a circle intersect internally or externally, then the products of the lengths of segments are equal.

Hence, from figure,

PA.PB = PC.PD …..(i)

Given,

PC = 15 cm and CD = 7 cm

From figure,

PD = PC - CD = 15 - 7 = 8 cm.

Let BP = x cm then AB = (12 - x) cm

Putting values in equation (i),

⇒ PA.PB = PC.PD
⇒ 12.x = 15.8
⇒ 12x = 120
⇒ x = 12012\dfrac{120}{12} = 10 cm.

AB = 12 - x = 12 - 10 = 2 cm.

Hence, Option 1 is the correct option.

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