Given information
The given radius line with slope intersects some of these circle.
To find: The smallest value of such that any line with slope intersect some of these circles.
Step-by-step explanation
Consider the line with slope and passing through the origin.
Equation to the normal to the line is .
These two lines are shown in the following diagram. Green line represents and brown line represents .
Figure
From the figure it is observed that, the points with integer coordinates are ……….etc.
Solve the equation and to solve point at which the line is tangent to the circle centered at.
Put into the equation .
Put into the equation .
Hence the point is .
Solve the equation and to solve point at which the line is tangent to the circle centered at .
Put in to the equation .
Put into the equation.
Hence the pointis
The slope of the line is given by the following equation.
Thus the slope of the line is, so.
Now solve this equation for.
Therefore, the minimum value ofisunits.