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Obtuse Triangle Ratio Condition

Source: Irish Mathematical Olympiad - Paper 1 - 2008 -Question 5

May 10, 2008
ratiogeometryparallelogramgeometry proposed

Problem Statement

A triangle ABC ABC has an obtuse angle at B B. The perpindicular at B B to AB AB meets AC AC at D D, and |CD| \equal{} |AB|. Prove that |AD|^2 \equal{} |AB|.|BC| if and only if \angle CBD \equal{} 30^\circ.
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