MathDB

1

Part of 2010 Oral Moscow Geometry Olympiad

Problems(2)

angle between AD and BE of equilaterals ABC and CDE

Source: 2010 Oral Moscow Geometry Olympiad grades 8-9 p1

8/16/2020
Two equilateral triangles ABCABC and CDECDE have a common vertex (see fig). Find the angle between straight lines ADAD and BEBE. https://1.bp.blogspot.com/-OWpqpAqR7Zw/Xzj_fyqhbFI/AAAAAAAAMao/5y8vCfC7PegQLIUl9PARquaWypr8_luAgCLcBGAsYHQ/s0/2010%2Boral%2Bmoscow%2Bgeometru%2B8.1.gif
geometryanglesEquilateral
convex cyclic n-gon cut into equal triangles by non-intersecting diagonals

Source: 2010 Oral Moscow Geometry Olympiad grades 10-11 p1

5/8/2020
Convex nn-gon PP, where n>3n> 3, is cut into equal triangles by diagonals that do not intersect inside it. What are the possible values of nn if the nn-gon is cyclic?
geometrycombinatorial geometrycombinatoricsCyclicpolygonconvex polygon