By Amber Krug
Given any triangle ABC and point P, we have:
My conjecture is that AF * CE * BD = 1.
FB EA DC
We can see this by constructing similar triangles and substituting the resulting similar ratios in to see that the product is in fact 1.
The ratio of the areas of triangles ABC and DEF will always be greater than or equal to 4. Click here to see when the ratio is greater than 4. The ratio is equal to 4 when triangle DEF is the medial triangle of ABC.