Intuitionism and circles I know next to nothing about intuitionism, so my question is probably silly :) As I understand from Wikipedia, intuitionism (at least finitism) doesn't 'trust' in the existence of irrational numbers, because they cannot be constructed (at least in finite number of steps). How does it deal with circles then? Or, even better, how does it deal with bilateral right triangles? Do such things exist in this framework? Do metric concepts exist at all?

Constructive mathematics allows irrational numbers and much more, including of course circles. See the books by Bishop and his followers on constructive analysis. Constructivism is often identified with intuitionism but it's not the same thing. See also this review of a book by Bridger.