question_answer

If the pair of tangents are drawn from origin O to the circle \[{{x}^{2}}+{{y}^{2}}-6x-8y+2=0\], meets the circle at A and B, then the length of AB is

A)  11                               

B)  \[\frac{4}{5}\sqrt{21}\]

C)  \[\sqrt{\frac{17}{3}}\]                          

D)  \[\frac{\sqrt{21}}{5}\]

Correct Answer: B

Solution :

Equation of chord of contact AB is \[3x+4y-21=0\] \[\therefore \,CM\,=\frac{4}{5}\] \[\therefore \,AM=\sqrt{4-C{{M}^{2}}}\,=\frac{2}{5}\,\sqrt{21}\] \[\therefore \,AB\,=\frac{4}{5}\,\sqrt{21}\]