Practice library
Problems
1Prove that among all triangles with one and the same perimeter, the equilateral triangle has the largest area.Open2In a convex hexagon \(ABCDEF\), each of the two diagonals \(AD\) and \(BE\) divides the hexagon into two pieces of equal area. Prove that the quadrilateral \(BDEA\) is a trapezoid.3Two concentric circles \(k_1\) and \(k_2\) have radii \(a\) and \(b\). Consider all rectangles that have two vertices on \(k_1\) and the remaining two vertices on \(k_2\). Determine the rectangle of largest …
Showing 3 of 651 - problem statements are free for everyone.