Spartan king

Menelaus, an ancient Greek mathematician, first proved Menelaus theorem. It is pointed out that if a straight line intersects with three sides AB, BC, CA of △ABC or its extension lines at points F, D and E, then AF/FB×BD/DC×CE/EA= 1.

Cheval theorem

Let o be any point in △ABC,

A0, B0 and c0 intersect at D, E and F respectively, then

BD/DC*CE/EA*AF/FB= 1

Let's start with these two. Ask me if you are interested. I am a senior three student, and I also have a math contest.