(a) Let ABC be any triangle. Let X,Y,Z be points on the sides BC,CA,AB respectively.
Suppose that BX≤XC,CY≤YA,AZ≤ZB. Show that the area of the triangle XYZ \geq 1\slash 4 times the area of ABC.
(b) Let ABC be any triangle, and let X,Y,Z be points on the sides BC,CA,AB respectively. Using (a) or by any other method, show: One of the three corner triangles AZY,BXZ,CYX has an area ≤ area of the triangle XYZ. Putnamgeometryareatriangle inequalityarea of a triangle