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Part of 2006 Portugal MO

Problems(1)

perpendicular wanted, inside an equilateral 2006 Portugal p2

Source:

10/13/2020
In the equilateral triangle [ABC],D[ABC], D is the midpoint of [AC],E[AC], E and the orthogonal projection of DD over [CB][CB] and FF is the midpoint of [DE][DE]. Prove that [FB][FB] and [AE][AE] are perpendicular. https://1.bp.blogspot.com/-TjSyQotGIOM/X4XMolaXHvI/AAAAAAAAMng/cVsHfl-lrXAFE5LMdosE6vqK1Tf-8WOQgCLcBGAsYHQ/s0/2006%2Bportugal%2Bp2.png
geometryEquilateralperpendicular