Question : A is a point outside of a circle with centre O. AP and AQ are two tangents of the circle. If AP = a2 + 14 and AQ = 239, then what is the value of a?
Option 1: 22
Option 2: 13
Option 3: 15
Option 4: 14
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Correct Answer: 15
Solution :
Given,
Length of AP = a
2
+ 14
Length of AQ = 239
We know that tangents drawn from an external point to a circle are equal
⇒ AP = AQ
⇒ a
2
+ 14 = 239
⇒ a
2
= 225
⇒ a = $\small\sqrt{225}$
⇒ a = 15
Hence, the correct answer is 15.
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