Problem

Source: Morocco 2011

Tags: geometry, ratio, angle bisector, geometry unsolved



Let ABC be a triangle with area 1 and P the middle of the side [BC]. M and N are two points of [AB]{A,B} and [AC]{A,C} respectively such that AM=2MB andCN=2AN. The two lines (AP) and (MN) intersect in a point D. Find the area of the triangle ADN.