A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{2}\]
Correct Answer: C
Solution :
Length of both tangents is given by \[\sqrt{{{S}_{1}}}\] i.e. \[\sqrt{75}\] or \[5\sqrt{3}\] and radius of the circle is \[\sqrt{36+64-75}\] or 5. Hence angle between the tangents is given by \[2{{\tan }^{-1}}\left( \frac{5}{5\sqrt{3}} \right)\] or\[\frac{\pi }{3}\].
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