Problems

Let \(ABCDE\) be a regular pentagon. The point \(G\) is the midpoint of \(CD\), the point \(F\) is the midpoint of \(AE\). The lines \(EG\) and \(BF\) intersect at the point \(H\). Find the angle \(EHF\).

A paper band of constant width is tied into a simple knot and tightened. Prove that the knot has the shape of a regular polygon.