Solution to the Napoleon's problem and one more not so typical construction problem

A few days ago I posted the following problem, that many books called the Napoleon's problem.

Given a segment of the length one, construct a segment of the length $\sqrt{2}$ units using a compass only.

Most people start with trying to construct a triangle with the sides 1, 1,  $\sqrt {2}$.  But this does not work for compass only construction.  Instead, it is much easier to construct a triangle $\sqrt{3}$, $\sqrt{3}$, 2, as shown below.

Step by step:

1. Draw a circle of radius 1 with a center at arbitrary point A.

2. Choose arbitrary point B on this circle.  Draw a circle of radius 1 with the center at B.

3. The second circle intercepts the first one at points C and D.  CD = $\sqrt{3}$

4. Draw the third unit circle with the center at C.  It intercepts the first one at B and E.  DE = 2.

5. Draw two circles of radius $\sqrt{3}$ with centers at D and E.  The distance from any of two points of their intersection to A is equal to $\sqrt{2}$.

The picture was made with Geogebra, and I apologize for its quality due to my first try of this program.

And at the end one more construction problem that involves both traditional instruments - straight edge and compass.  

Given three arbitrary parallel lines on a plane, construct an equilateral triangle with vertices on these lines.