MathDB

2

Part of 2023 Oral Moscow Geometry Olympiad

Problems(2)

rectangle with ratio of sides \sqrt2 by square sheet of paper

Source: Oral Moscow Geometry Olympiad 2023 8-9 p2

2/26/2024
There is a square sheet of paper. How to get a rectangular sheet of paper with an aspect ratio equal to 2\sqrt2? (There are no tools, the sheet can only be bent.)
ratiogeometryrectanglepaper
Find the locus

Source: Oral Moscow geometry olympiad 2023 10-11.2

4/20/2023
Points X1X_1 and X2X_2 move along fixed circles with centers O1O_1 and O2O_2, respectively, so that O1X1∥O2X2O_1X_1 \parallel O_2X_2. Find the locus of the intersection point of lines O1X2O_1X_2 and O2X1O_2X_1.
geometry