A rectangle is made up from six squares. Find side length of the largest square if side length of the smallest square is 1.
This shape below is made up from squares.
Find side length of the bottom square if side length of the smallest square is equal to 1.
You are given a convex quadrilateral. Is it always possible to cut out a parallelogram out of the quadrilateral such that three vertices of the new parallelogram are the vertices of the old quadrilateral?
The area of a rectangle is 1 cm\(^2\). Can its perimeter be greater than 1 km?
9 straight lines each divide a square into two quadrilaterals, with their areas having a ratio of \(2:3\). Prove that at least three of the nine lines pass through the same point.
Prove that a convex quadrilateral \(ICEF\) can contain a circle if and only if \(IC+EH = CE+IF\).
A square of side 15 contains 20 non-overlapping unit squares. Prove that it is possible to place a circle of radius 1 inside the large square, so that it does not overlap with any of the unit squares.
In a regular 1981-gon 64 vertices were marked. Prove that there exists a trapezium with vertices at the marked points.