Draw certain lines using a triangle's three sides or three angles, and remarkably, those lines always meet at one point. Such a point is called a "center" of the triangle. Freely drag vertices A, B, and C to change the triangle's shape, and see exactly how each of the five centers is constructed.
A triangle contains points with very different characters, depending on where certain special lines drawn from its sides or angles happen to meet. The point where the perpendicular bisectors of the three sides meet (the circumcenter) is equidistant from all three vertices, so a circle centered there wraps the triangle exactly. The point where the lines splitting the three angles in half meet (the incenter), on the other hand, is equidistant from all three sides, making it the center of a circle that fits perfectly inside the triangle.
Here's a fun fact — the centroid, circumcenter, and orthocenter always lie on a single straight line (the Euler line), no matter how the triangle's shape changes. What's more, the centroid always sits at the point that divides the distance from the circumcenter to the orthocenter in a 1:2 ratio.
How to use it — Pick a center one at a time from the tabs below and compare how the lines are drawn, then drag vertices A, B, and C with your finger or mouse and see whether the center's position ever moves outside the triangle.