question_answer

If the chord y=mx+1 of the circle\[{{x}^{2}}+{{y}^{2}}=1\]subtends an angle of measure \[45{}^\circ \]at the major segment of the circle, then the value of m is

A) \[2\pm \sqrt{2}\]        

B) \[-2\pm \sqrt{2}\]

C) \[-1\pm \sqrt{2}\]       

D) None of these

Correct Answer: C

Solution :

[c] From the figure, \[OB=1,\,OD=\frac{1}{\sqrt{2}}\] Also, \[OD=\frac{\left| m(0)-0+1 \right|}{\sqrt{{{m}^{2}}+1}}\] So, we have \[\frac{\left| m(0)-0+1 \right|}{\sqrt{{{m}^{2}}+1}}=\frac{1}{\sqrt{2}}\] \[\therefore m=\pm 1\]