TITLE: Compass and straightedge difficult construction
QUESTION [5 upvotes]: I don't know if there is any way to geometrically construct a circle with a given length of circumference.
I have tried several options but don't seem to get it.
Any construction I think of, involves π, which I think is impossible to construct geometrically, right?
Any help?

REPLY [2 votes]: This construction is equivalent to squaring the circle, so there is no such construction:

In 1882, the task was proven to be impossible, as a consequence of the
  Lindemann–Weierstrass theorem which proves that $\pi$ is a
  transcendental, rather than an algebraic irrational number; that is,
  it is not the root of any polynomial with rational coefficients.

https://en.wikipedia.org/wiki/Squaring_the_circle