MathDB

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

Problem Statement