In a tetrahedron VABC, let I be the incenter and A′,B′,C′ be arbitrary points on the edges AV,BV,CV, and let Sa,Sb,Sc,Sv be the areas of triangles VBC,VAC,VAB,ABC, respectively. Show that points A′,B′,C′,I are coplanar if and only if A′VAA′Sa+B′VBB′Sb+C′VCC′Sc=Sv tetrahedroncoplanar3D geometrygeometryincentertriangle area