MathDB

2

Part of 2013 Tuymaada Olympiad

Problems(2)

Equal angles in a rhombus

Source: Tuymaada 2013, Day 1, Problem 2 Seniors

7/24/2013
Points XX and YY inside the rhombus ABCDABCD are such that YY is inside the convex quadrilateral BXDCBXDC and 2∠XBY=2∠XDY=∠ABC2\angle XBY = 2\angle XDY = \angle ABC. Prove that the lines AXAX and CYCY are parallel.
S. Berlov
geometryrhombusgeometric transformationreflectionsymmetrytrapezoidtrigonometry
Metric relation in a hexagon

Source: Tuymaada 2013, Day 1, Problem 2 Juniors

7/20/2013
ABCDEFABCDEF is a convex hexagon, such that in it AC∥DFAC \parallel DF, BD∥AEBD \parallel AE and CE∥BFCE \parallel BF. Prove that AB2+CD2+EF2=BC2+DE2+AF2.AB^2+CD^2+EF^2=BC^2+DE^2+AF^2.
N. Sedrakyan
geometryvectorratiogeometry proposed