MathDB

The medians

AD, BE

and

CF

of triangle

ABC

intersect at

G

. Let

P

be a point lying in the interior of the triangle, not belonging to any of its medians. The line through

P

parallel to

AD

intersects the side

BC

A_{1}

. Similarly one defines the points

B_{1}

and

C_{1}

. Prove that

\overline{A_{1}D}+\overline{B_{1}E}+\overline{C_{1}F}=\frac{3}{2}\overline{PG}

Problem Statement