MathDB

Let

B

and

C

be two fixed points in the plane. For each point

A

of the plane, outside of the line

BC

, let

G

be the barycenter of the triangle

ABC

. Determine the locus of points

A

such that

\angle BAC + \angle BGC = 180^{\circ}

.
Note: The locus is the set of all points of the plane that satisfies the property.

Problem Statement