Please help in this difficult math geometry quiz.

 From:  Psygorn (DRILLBIT)
11167.52 In reply to 11167.1 
Hello Elang,

I wonder how I missed your post! As I love geometric puzzles!

I think by now you have solved your puzzle, However I would like to examine a possible solution myself, so, please answer the following questions:

> So we provided with 3 lines:
> - 1 horizontal blue line with length of X√2
> - 2 magenta lines with length of X

> The task is to arrange them in specific ways so that: they form a continuous polylines with each endpoints are exactly on a perfect circle circumverence (red circle), like in the provided illustration (it's actually not an acurate drawing I
> made in Moi). The real task is to form a pentagon with 4 magenta lines (length = x) and 1 blue lines (length = x√2), but I believe we can ignore the other 2 since they'll be added later by mirroring the 2 existing magenta lines horizontaly.

1- the pentagon should be regular or it could be irregular? (I know if the blue line is going to be the base of the pentagon then we are talking about irregular pentagon I also know u have mentioned it! however, I need to be sure.)
2- Tell me if we are provided by all the mentioned lines. (or should we make a line from other line? for example blue from red?)
3- Tell me about the initial position of the 3 lines!

- Psygorn