MathDB

2

Part of 2016 Oral Moscow Geometry Olympiad

Problems(2)

ratio of sides in a rectangle, broken line with right angles

Source: 2016 Oral Moscow Geometry Olympiad grades 8-9 p2

7/30/2019
In the rectangle there is a broken line, the neighboring links of which are perpendicular and equal to the smaller side of the rectangle (see the figure). Find the ratio of the sides of the rectangle. https://2.bp.blogspot.com/-QYj53KiPTJ8/XT_mVIw876I/AAAAAAAAKbE/gJ1roU4Bx-kfGVfJxYMAuLE0Ax0glRbegCK4BGAYYCw/s1600/oral%2Bmoscow%2B2016%2B8.9%2Bp2.png
ratiogeometryrectangle
parallel wanted starting with a regular heptagon

Source: 2016 Oral Moscow Geometry Olympiad grades 10-11 p2

7/29/2019
A regular heptagon A1A2A3A4A5A6A7A_1A_2A_3A_4A_5A_6A_7 is given. Straight A2A3A_2A_3 and A5A6A_5A_6 intersect at point XX, and straight lines A3A5A_3A_5 and A1A6A_1A_6 intersect at point YY. Prove that lines A1A2A_1A_2 and XYXY are parallel.
geometryHeptagonparallel