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.
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.