MathDB

5

Part of 2022 Novosibirsk Oral Olympiad in Geometry

Problems(3)

area, 2 equal rectangles (2022 Novosibirsk Oral Geo Oly 7.5)

Source:

9/2/2023
Two equal rectangles of area 1010 are arranged as follows. Find the area of the gray rectangle. https://cdn.artofproblemsolving.com/attachments/7/1/112b07530a2ef42e5b2cf83a2cb9fb11dfc9e6.png
geometryrectanglearea
area by 2 isosceles triangles of same area (2022 Novosibirsk Oral Geo Oly 8.5)

Source:

9/2/2023
Two isosceles triangles of the same area are located as shown in the figure. Find the angle xx. https://cdn.artofproblemsolving.com/attachments/a/6/f7dbfd267274781b67a5f3d5a9036fb2905156.png
geometryareaisosceles
triangle split into 22 triangles with 22^o (2022 Novosibirsk Oral Geo Oly 9.5)

Source:

9/3/2023
Prove that any triangle can be divided into 2222 triangles, each of which has an angle of 22o22^o, and another 2323 triangles, each of which has an angle of 23o23^o.
geometrycombinatorial geometry