This write-up explores aspects of a triangle with a random point p on the interior of the triangle. This write-up has three parts. The first looks at the how the products of the parts of the sides are related. The second is a proof of the exploration done in part A. The third explores the ratios of the two triangles. The write-up is based on the following picture.
Click on the following links for the discussions of the different parts.
Part A: Exploring the products: (AF)(BD)(CE) and (AE)(BF)(CD).
Part B: Proof of the conjecture that made in Part A.
Part C: The ratio of triangle ABC to triangle DEF.