The fourth quadrant tangent:
Distance from the center to the tangent point: 2
Because y=x, it can be assumed that the linear equation is y=x+c after translation (because the slope is unchanged, only the intersection of x and y axes is changed).
Because the coordinates of the tangent point are (root number 2,-root number 2), that is, (1.4 14,-1.4 14).
So substitute the tangent point into the equation y = x+c.
-radical number 2 = radical number 2+c
The radical number 2 with C=-2 (2.828)
So y=x-2.828.
So the intersection with the x axis (2.828,0)
Therefore, when the tangent line is in the fourth image limit OP=2.828,
Tangent of the second quadrant:
Similarly, the linear equation can still be obtained as y=x+2.828.
So op is still equal to 2.828 (the actual intersection is (-2.828,0), but considering that op is the distance, it is 2.828).
Therefore, regardless of the translation, the value of OP can only be: 0 to 2.828.