1

Part of 2007 Oral Moscow Geometry Olympiad

Problems(2)

covering a cube os edge 1 with a strip 12x1

Source: 2007 Oral Moscow Geometry Olympiad grades 8-9 p1

Given a rectangular strip of measure

12 \times 1

. Paste this strip in two layers over the cube with edge

1

(the strip can be bent, but cannot be cut).
(V. Shevyakov)

geometry3D geometrycube

triangle cut in 5 triangles similar to the big, is it right one?

Source: 2007 Oral Moscow Geometry Olympiad grades 10-11 p1

The triangle was divided into five triangles similar to it. Is it true that the original triangle is right-angled?
(S. Markelov)

geometrysimilar trianglesright triangle