Question : In the figure, chords AB and CD of a circle intersect externally at P. If AB = 4 cm, CD = 11 cm and PD =15 cm, then the length of PB is:
Option 1: 10 cm
Option 2: 8 cm
Option 3: 14 cm
Option 4: 12 cm
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Correct Answer: 10 cm
Solution :
AB and CD are two chords of a circle intersecting externally at P
AB = 4 cm, CD = 11 cm and PD = 15 cm
If two chords AB and CD intersect at outer point P then,
PA × PB = PC × PD
Let the length of PA be $x$
PC = PD - CD
= 15 - 11
= PC = 4 cm
According to the question
PA × PB = PC × PD
⇒ $x$ × ($x$ + 4) = 15 × 4
⇒ $x$ = 6
PB = PA + AB
= 6 + 4
= 10
$\therefore$ The length of PB is 10 cm.
Hence, the correct answer is 10 cm.
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