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<A=120^o, median AD perpendicular to side AB (Greece Junior 2011)

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July 14, 2019
geometryperpendicularcircumcircle

Problem Statement

Let ABCABC be a triangle with ∠BAC=120o\angle BAC=120^o, which the median ADAD is perpendicular to side ABAB and intersects the circumscribed circle of triangle ABCABC at point EE. Lines BABA and ECEC intersect at ZZ. Prove that a) ZD⊥BEZD \perp BE b) ZD=BCZD=BC
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