MathDB

3

Part of 2002 Greece National Olympiad

Problems(1)

In a triangle.

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

11/18/2005
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.
geometrycircumcircletrigonometryinequalitiesfunctiongeometry proposed