MathDB

2

Part of 2010 Oral Moscow Geometry Olympiad

Problems(2)

paperfolding a square paper of side 1 to measure a distance 5/6

Source: 2010 Oral Moscow Geometry Olympiad grades 8-9 p2

8/16/2020
Given a square sheet of paper with side 11. Measure on this sheet a distance of 5/6 5/6. (The sheet can be folded, including, along any segment with ends at the edges of the paper and unbend back, after unfolding, a trace of the fold line remains on the paper).
geometrypaperfoldingsquaredistance
parallel lines by projections inside a cyclic ABCD

Source: 2010 Oral Moscow Geometry Olympiad grades 10-11 p2

5/8/2020
Quadrangle ABCDABCD is inscribed in a circle. The perpendicular from the vertex CC on the bisector of ∠ABD\angle ABD intersects the line ABAB at the point C1C_1. The perpendicular from the vertex BB on the bisector of ∠ACD\angle ACD intersects the line CDCD at the point B1B_1. Prove that B1C1∥ADB_1C_1 \parallel AD.
geometrycyclic quadrilateralperpendicularparallel