Τρίτη, 10 Οκτωβρίου 2017

2008 JBMO Shortlist G6

Let $ABC$ be a triangle with $\angle A<{{90}^{o}} $. Outside of a triangle we consider isosceles triangles $ABE$ and $ACZ$ with bases $AB$ and $AC$, respectively. If the midpoint $D$ of the side $BC$ is such that $DE \perp DZ$ and $EZ = 2 \cdot ED$, prove that $\angle AEB = 2 \cdot \angle AZC$ .

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