I will begin this final assignment by drawing an arbitrary triangle ABC and an arbitrary point P in the middle. I will then draw lines AP, BP, and CP where the lines hit the opposite sides of the triangle will be my points D, E, and F.

The ratio is 1 but I have not moved my point P. Let's see what happens when P is moved towards the left.

The ratio is still 1. What will happen if I move my point P to the right?

The ratio is still 1. Let's investigate why this is the case.

Now lets see if the ratio holds true when P is outside of the triangle.

When P is outside of the triangle the relationship does not hold true.