question_answer

The range of values of r for which the point\[\left( -5+\frac{r}{\sqrt{2}},-3+\frac{r}{\sqrt{2}} \right)\] is an interior point of the major segment of the circle \[{{x}^{2}}+{{y}^{2}}=16,\] cut off by the line \[x+y=2,\] is

A)  \[(-\,\infty ,\,\,5\,\sqrt{2})\]

B)  \[(4\,\sqrt{2}-\sqrt{14},\,\,5\,\sqrt{2})\]

C)  \[(4\,\sqrt{2}-\sqrt{14},\,\,4\,\sqrt{2}+\sqrt{14})\]

D)  \[(4\,\sqrt{2}-\sqrt{14},\,\,4\,\sqrt{2}-\sqrt{14})\]

E)  None of these