# Question on geometry triangle and incenter [duplicate]

Let ABC be a triangle. Let B' and C' denotes respectively the reflection of B and C in the internal angle bisectors of angle A. How do I prove that the triangles ABC and AB'C' have same incenter.

Triangles $ABC$ and $AB'C'$ are symmetric over the angle bisector of $A$ and hence so do their incenters. Also since the incenters lies on the bisector they must be the same point.