2

Part of 2006 Oral Moscow Geometry Olympiad

Problems(2)

ratio of sidelengths of rectangle circumscribed in L shape

Source: 2006 Oral Moscow Geometry Olympiad grades 8-9 p2

Determine the ratio of the sides of the rectangle circumscribed around a corner of five cells (see figure).
(M. Evdokimov) https://cdn.artofproblemsolving.com/attachments/f/f/9c3e345f33cabbbd83f65d7240aac29a163b19.png

ratiogeometryrectangle

any 3 out of 6 segments form a triangle, what about a tetrahedron?

Source: 2006 Oral Moscow Geometry Olympiad grades 10-11 p2

Six segments are such that any three can form a triangle. Is it true that these segments can be used to form a tetrahedron?
(S. Markelov)

geometry3D geometrytetrahedrontriangle inequality