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Ratio between parallel segments in an isosceles triangle

Source: Nordic MO 2011 Q2

April 21, 2013
ratiogeometry unsolvedgeometry

Problem Statement

In a triangle ABCABC assume AB=ACAB = AC, and let DD and EE be points on the extension of segment BABA beyond AA and on the segment BCBC, respectively, such that the lines CDCD and AEAE are parallel. Prove CD \ge \frac{4h}{BC}CE, where hh is the height from AA in triangle ABCABC. When does equality hold?
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