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2013 HMMT Guts #14: Angle Bisectors Galore

Source:

March 26, 2013
HMMTtrigonometryratiogeometryangle bisector

Problem Statement

Consider triangle ABCABC with ∠A=2∠B\angle A=2\angle B. The angle bisectors from AA and CC intersect at DD, and the angle bisector from CC intersects AB‾\overline{AB} at EE. If DEDC=13\dfrac{DE}{DC}=\dfrac13, compute ABAC\dfrac{AB}{AC}.
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