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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