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A triangle ABC with ABC = 2<ACB

Source: Romanian District Olympiad 2006, Grade 7, Problem 2

March 11, 2006
inequalitiestrigonometry

Problem Statement

In triangle ABCABC we have ∠ABC=2∠ACB\angle ABC = 2 \angle ACB. Prove that a) AC2=AB2+AB⋅BCAC^2 = AB^2 + AB \cdot BC; b) AB+BC<2⋅ACAB+BC < 2 \cdot AC.
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