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?

15

Concept Used

Tangents drawn from an external point to a circle are equal

Solution

= AP = AQ

= \( { a}^{2 } \) + 14 = 239

= \( { a}^{2 } \) = 225

= a = 15

Therefor, the answer is 15.