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

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July 14, 2019
geometryrectangleEquilateralequal segmentsperpendicular

Problem Statement

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
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