1. ## Construction

Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.

2. Originally Posted by mathfun
Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.
Is it allowed to use compasses?

3. Yeap

4. Originally Posted by mathfun
Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.
Ok, I have done it. Now what?

5. Originally Posted by mathfun
Given two points on the plane. Bring the line that connects them if the ruler you have is smaller than the distance between those points.
1. I assume that the compasses open more than half of the distance between the points A and B.

2. Draw circles around A and B with the utmost opening of the compasses. These 2 circles have to intersect in 2 points P and Q.

3. The midpoint of PQ is the midpoint of AB too. Can you finish the construction now?

6. Originally Posted by earboth
Can you finish the construction now?
If not, we can repeat the procedure recursively, right (between A/B and midpoint of AB)?

7. Originally Posted by alexmahone
If not, we can repeat the procedure recursively, right (between A/B and midpoint of AB)?
Correct!

It is only necessary that the 2 circle-lines intersect so that you can construct midpoints between midpoints between ...