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Part of 2001 JBMO ShortLists

Problems(1)

The point E on AB=AC - JBMO Shortlist

Source:

10/30/2010
Consider a triangle ABCABC with AB=ACAB=AC, and DD the foot of the altitude from the vertex AA. The point EE lies on the side ABAB such that ∠ACE=∠ECB=18∘\angle ACE= \angle ECB=18^{\circ}.
If AD=3AD=3, find the length of the segment CECE.
trigonometrygeometryangle bisectortrig identitiesLaw of Cosinesgeometry proposed