MathDB

Let

ABC

be an isosceles triangle with

AB=AC

. On the extension of the side

{CA}

we consider the point

{D}

such that

{AD<AC}

. The perpendicular bisector of the segment

{BD}

meets the internal and the external bisectors of the angle

\angle BAC

at the points

{E}

and

{Z}

, respectively. Prove that the points

{A, E, D, Z}

are concyclic.

Problem Statement