Olympiad problems

AND:

OR:

NO:

Found problems: 27

May Olympiad L2 - geometry, 2023.4

Matías has a rectangular sheet of paper $ABCD$, with $AB<AD$.Initially, he folds the sheet along a straight line $AE$, where $E$ is a point on the side $DC$ , so that vertex $D$ is located on side $BC$, as shown in the figure. Then folds the sheet again along a straight line $AF$, where $F$ is a point on side $BC$, so that vertex $B$ lies on the line $AE$; and finally folds the sheet along the line $EF$. Matías observed that the vertices $B$ and $C$ were located on the same point of segment $AE$ after making the folds. Calculate the measure of the angle $\angle DAE$. [img]https://cdn.artofproblemsolving.com/attachments/0/9/b9ab717e1806c6503a9310ee923f20109da31a.png[/img]

2016 Sharygin Geometry Olympiad, 5

Tags: geometry , paper , equilateral triangle

Three points are marked on the transparent sheet of paper. Prove that the sheet can be folded along some line in such a way that these points form an equilateral triangle. by A.Khachaturyan