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

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

• I would like to see a picture of a circle intersecting a line at three different points. – Vasya Oct 24 '18 at 18:53
• The points are 2 or 3? – Federico Fallucca Oct 24 '18 at 18:53
• I HAVE ADDED THE SHAPE! – user602338 Oct 24 '18 at 18:59
• The question is not quite clear. If it's exactly three points on both lines combined then the only choice is $2$. – Vasya Oct 24 '18 at 18:59
• So now let's take a look at picture. Would you explain completely?! – user602338 Oct 24 '18 at 19:00

## 3 Answers

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... • Sorry what?! I didnt understand you here! – user602338 Oct 24 '18 at 19:05
• You mean option 2? – user602338 Oct 24 '18 at 19:06
• The only way that the circle touches the two lines a odd number of times is if it is tangent to one of the lines. There is only one value of L, where it will intersect one line and be tangent to the other. – Doug M Oct 24 '18 at 19:07

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.

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 $$L=2$$