A) \[\sqrt{5}\]unit
B) \[\sqrt{10}\]unit
C) \[\sqrt{15}\]unit
D) \[\sqrt{20}\]unit
Correct Answer: B
Solution :
The equation of tangents are given \[x+3y-5=0\] ?(i) and \[2x+6y+30=0\] or \[x+3y+15=0\] ?(ii) We know that the distance between two parallel lines is \[\left| \frac{{{c}_{1}}-{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}}} \right|\] \[=\left| \frac{-5-15}{\sqrt{1+9}} \right|\] \[=\frac{20}{\sqrt{10}}\] Hence, the radius of circle \[=\frac{1}{2}\times \frac{20}{\sqrt{10}}\] \[=\frac{10}{\sqrt{10}}\] \[=\sqrt{10}\]unit Note: The distance between two parallel lines is\[\frac{|{{c}_{1}}-{{c}_{2}}|}{\sqrt{a_{1}^{2}+b_{1}^{2}}}.\]
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