We have 2 parallel lines $d$ and $d'$ and we wand calculate distance from point to the lines...(read the details)

Question

There are 2 parallel lines $d$ and $d'$. The point $O$ is between these lines and space from $O$ to $d$ is $1$ and to $d'$ is $2$. We know that there are 3 points on one of these lines that their distance from the point $O$ is $L$. So now find $L$. Options are $1 or 2 or 3 or 4$ How can I calculate $L$?! the shape is here

Answer 1

If L is too small, you don't intersect both lines. Maybe not even one line.

If L is too big, you interesect both lines twice.

But if L is just right...

Answer 2

Hint:

The question can be formulated in this way:

Calculate the radius of the circonference that it is indentified by these points.

Two of these points are in one of the two lines and the part of the lines between that points it will be a rope for the cirumference. The lines of the other point will be tangent to the circumference because otherwise you could have 4 points that are the same distance from O.

Answer 3

If all three points are on one of the lines, I do not think we can have an answer.

On the other hand if we have three points on lines then with a distance of $L=2$ we can have 2 points on the line $d$ and we already have a point on $d'$ which makes it the three points on two lines.

Thus if there is an answer it better be $L=2$