Let M be an interior point of tetrahedron VABC. Denote by A1,B1,C1 the points of intersection of lines MA,MB,MC with the planes VBC,VCA,VAB, and by A2,B2,C2 the points of intersection of lines VA1,VB1,VC1 with the sides BC,CA,AB.(a) Prove that the volume of the tetrahedron VA2B2C2 does not exceed one-fourth of the volume of VABC.(b) Calculate the volume of the tetrahedron V1A1B1C1 as a function of the volume of VABC, where V1 is the point of intersection of the line VM with the plane ABC, and M is the barycenter of VABC. geometry3D geometrytetrahedronfunctiongeometry unsolved