Make a vertical line from the center of the circle to a straight line y=x+ 1. The vertical foot is-
The shortest tangent drawn by a vertical ruler is the root number 7.
Because the radius is fixed, the tangent is the shortest only if the distance from the center of the circle to the straight line is the shortest.
PS: I don't know if the calculation is correct because I am lazy. LZ will do its own calculations ... sorry. ...