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In a triangle.

Source: Greece National Olympiad 2002 , Seniors , Problem 3.

November 18, 2005
geometrycircumcircletrigonometryinequalitiesfunctiongeometry proposed

Problem Statement

In a triangle ABCABC we have ∠C>100\angle C>10^0 and ∠B=∠C+100.\angle B=\angle C+10^0.We consider point EE on side ABAB such that ∠ACE=100,\angle ACE=10^0, and point DD on side ACAC such that ∠DBA=150.\angle DBA=15^0. Let Z≠AZ\neq A be a point of interection of the circumcircles of the triangles ABDABD and AEC.AEC.Prove that ∠ZBA>∠ZCA.\angle ZBA>\angle ZCA.
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