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Paraguayan National Olympiad 2008, Level 3, Problem 3

Source:

August 31, 2014
Asymptote

Problem Statement

Let ABCABC be a triangle, where AB=ACAB = AC and BC=12BC = 12. Let DD be the midpoint of BCBC. Let EE be a point in ACAC such that DE⊥ACDE \perp AC. Let FF be a point in ABAB such that EF∥BCEF \parallel BC. If EC=4EC = 4, determine the length of EFEF.
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