MathDB

Let

ABC

be a triangle. For a point

P

in its interior, we draw the threee lines through

P

parallel to the sides of the triangle. This partitions

ABC

in three triangles and three quadrilaterals.
Let

V_A

be the area of the quadrilateral which has

A

as one vertex. Let

D_A

be the area of the triangle which has a part of

BC

as one of its sides. Define

V_B, D_B

and

V_C, D_C

similarly.
Determine all possible values of

\frac{D_A}{V_A}+\frac{D_B}{V_B}+\frac{D_C}{V_C}

, as

P

varies in the interior of the triangle.

Problem Statement