Question : In the given figure, the diameter AB and chord CD of a circle meet at P. PT is tangent to the circle at T. If CD = 8 cm, PD = 10 cm, and PB = 8 cm, find AB.
Option 1: 14.5 cm
Option 2: 22.5 cm
Option 3: 12 cm
Option 4: 8 cm
Correct Answer: 14.5 cm
Solution :
Given: CD = 8 cm, PD = 10 cm, and PB = 8 cm
$\therefore$ PC = CD + PD = 8 + 10 = 18 cm
If two chords, AB and CD, of a circle intersect at a point P outside the circle,
PA $\times$ PB = PC $\times$ PD
⇒ PA × 8 = 18 ×10
$\therefore$ PA = 22.5 cm
The length of AB is given as,
AB = PA – PB
⇒ AB = 22.5 – 8
$\therefore$ AB = 14.5 cm
Hence, the correct answer is 14.5 cm.
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