If you were to throw a handful of pick-up sticks down onto the floor, you might notice that no three of them intersected each other in exactly one point. Three such lines are shown in the picture below. Their intersection point G is called the circumcenter of triangle ABC as it is the center of the circle circumscribing triangle ABC .
Any line joining a vertex of a triangle to a point on the opposite side is called a cevian .
Many of these special points are related to one another in fascinating ways. They will be the doorways through which you will begin your journey of exploration.