A) 0
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{2}\]
Correct Answer: D
Solution :
Any line through (0, 0) be \[y-mx=0\] and it is a tangent to circle\[{{(x-7)}^{2}}+{{(y+1)}^{2}}=25\], if \[\frac{-1-7m}{\sqrt{1+{{m}^{2}}}}=5\Rightarrow m=\frac{3}{4},\ -\frac{4}{3}\]. Therefore, the product of both the slopes is -1. i.e., \[\frac{3}{4}\times -\frac{4}{3}=-1\]. Hence the angle between the two tangents is\[\frac{\pi }{2}\].
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