about to only mathematics

Options

A. `( -oo,5sqrt(2))`
B. `(4sqrt(2)-sqrt(14),5sqrt(2))`
C. `(4sqrt(2)-sqrt(14),4sqrt(2)+sqrt(14))`
D. none of these

Answer

2

Explanation

The given point is an interior point. Therefore,
`(-5+(r )/(sqrt(2)))^(2)+(-3+(r )/(sqrt(2)))^(2)-16 lt 0`
or `r^(2)-8sqrt(2)r+18 lt0`
or `4 sqrt(2)-sqrt(14) lt r lt 4sqrt(2)+sqrt(14)` (1)
The point is in the major segment. Therefore, the center and the point are the same side of the line `x+y=2`. Thus,
`-5+(r )/(sqrt(2))-2+(r )/(sqrt(2))-2 lt0`
or `r lt 5 sqrt(2) ` (2) From (1) and (2), `4 sqrt(2)-sqrt(14) lt r lt 5 sqrt(2)`.