Question
Download Solution PDFIn 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:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
AB and CD are two chords of a circle intersect externally at P
AB = 4 cm, CD = 11 cm and PD = 15 cm
Formula used :
If two chords AB and CD intersect at outer point P then,
PA × PB = PC × PD
Calculations :
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) = 4 × 15
⇒ x = 6
PB = PA + AB
⇒ 6 + 4
⇒ 10
∴ The length of PB is 10 cm
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