Definition of incenter in US English:


(British incentre)


  • The center of the incircle of a triangle or other figure.

    • ‘Therefore, the hexagon lies on a circle centered at the incenter of that triangle.’
    • ‘Through each of its vertices draw a line perpendicular to the line joining that vertex with its incenter P. The four lines form a cyclic quadrilateral ABCD with perpendicular diagonals that pass through P.’
    • ‘Located where the bisectors of a triangle's three angles intersect, the incenter is the center of the largest circle that can be inscribed inside that triangle.’
    • ‘The results of one such program, SIXTRI, suggested that the incenters of the small triangles formed by three intersecting cevians through special points, lie on an ellipse, while their circumcenters lie on a conic.’
    • ‘In each of the three triangles pass a straight line through its incenter and circumcenter.’