The area of a rectangle is 1 cm\(^2\). Can its perimeter be greater than 1 km?
Ben is going to bend a square sheet of paper \(ABCD\). Ben calls the fold beautiful, if the side \(AB\) crosses the side \(CD\) and the four resulting rectangular triangles are equal. Before that, Jack selects a random point on the sheet \(F\). Find the probability that Ben will be able to make a beautiful fold through the point \(F\).
Prove that a convex quadrilateral \(ICEF\) can have a circle inscribed into it if and only if \(IC+EH = CE+IF\).