MathDB

Let

ABC

be a triangle such that

\measuredangle BAC = 60^{\circ}

. Let

D

and

E

be the feet of the perpendicular from

A

to the bisectors of the external angles of

B

and

C

in triangle

ABC

, respectively. Let

O

be the circumcenter of the triangle

ABC

. Prove that circumcircle of the triangle

BOC

has exactly one point in common with the circumcircle of

ADE

Problem Statement