Consider any triangle ABC. Using any point P inside the triangle draw lines AP, BP and CP extended to their intersections with the opposite sides in points D, E, and F, respectively.
First, explore (AF)(BD)(EC) and (FB)(DC)(EA) for various triangles and various locations of P.
Click here to open a GSP sketch that allows you to manipulate the location of p allowing the observation of the relationship.
Click HERE for that proof.
that when P is inside triangle ABC, the ratio of the areas of triangle ABC and triangle DEF is always greater than or equal to 4.
Click here for that investigation.
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