Mathematics
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
2 cm
4 cm
6 cm
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.](https://cdn1.knowledgeboat.com/img/mla10/q20-c15-mcq-circles-ml-aggarwal-solutions-icse-class-10-1200x753.png)
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 = = 10 cm.
AB = 12 - x = 12 - 10 = 2 cm.
Hence, Option 1 is the correct option.
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