# 2012-11 Dividing a circle

Let f be a continuous function from [0,1] such that f([0,1]) is a circle. Prove that there exists two closed intervals $$I_1, I_2 \subseteq [0,1]$$ such that $$I_1\cap I_2$$ has at most one point, $$f(I_1)$$ and $$f(I_2)$$ are semicircles, and $$f(I_1)\cup f(I_2)$$ is a circle.

GD Star Rating