MathDB

2

Part of 2010 Greece Junior Math Olympiad

Problems(1)

rectangle, equilateral, equal segments in extensions (Greece Junior 2010)

Source:

7/14/2019
Let ABCDABCD be a rectangle with sides AB=aAB=a and BC=bBC=b. Let OO be the intersection point of it's diagonals. Extent side BABA towards AA at a segment AE=AOAE=AO, and diagonal DBDB towards BB at a segment BZ=BOBZ=BO. If the triangle EZCEZC is an equilateral, then prove that: i) b=a3b=a\sqrt3 ii) AZ=EOAZ=EO iii) EO⊥ZDEO \perp ZD
geometryrectangleEquilateralequal segmentsperpendicular