In the following figure, PC = 9, PB = 12, PA = 18, and PF = 8. Then, find the length of DE.
Explanation:
If we consider the smaller circle, two secants are drawn from P.
∴ PC × PB = PF × PE
⇒ 9 × 12 = 8 × PE
⇒ PE = 27/2
Now, if we consider the bigger circle, two secants are drawn from P.
∴ PB × PA = PE × PD
⇒ 12 × 18 = 27/2 × PD
⇒ PD = 16
∴ DE = PD – PE = 16 – 27/2 = 16 – 13.5 = 2.5
Hence, 2.5.
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