In number theory, many problems are easy to state but difficult to solve within number theory.
Are there Elementary (solved and unsolved) problems from Euclid's geometry, which are difficult to solve only by Euclid's axioms or the newest Hilbert's axioms on geometry? Had Euclid or Archimedes posed such propositions which they couldn't prove?
(The most well known such questions are from Ruler and compass constructions, and doubling cube. I would like to see the problems, whose statements are like the propositions of Euclid, but whose proof requires non-geometry tools.)