Question : PM and PN are two tangents of a circle from an external point P. M and N are points on the circle. If PM = y2 – 9 and PN = 55, then what is the value of y?
Option 1: 64
Option 2: 17
Option 3: 8
Option 4: 12
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Correct Answer: 8
Solution :
PM and PN are two tangents of a circle from an external point P.
Given: PM = $\text{y}^2$ – 9 and PN = 55
Tangents are equal in length if drawn from an outside point on the circle.
According to the concept,
PM = PN
⇒ $\text{y}^2$ – 9 = 55
⇒ $\text{y}^2$ = 64
$\therefore$ y = 8
Hence, the correct answer is 8.
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