What do you notice about the three perpendicular bisectors?[br][br]What happens if you change the triangle into an acute triangle? Right triangle? Obtuse triangle?[br][br]Draw a circle with its center at the point you have created and the edge at point A, what do you notice?
All the perpendicular bisectors intersect at one place. This point is called the [b]circumcenter[/b], which is the center of the [b]circumcircle[/b] of the triangle. The circumcircle is a circle that only touches the triangle at the three vertices. This is called circumscribing and it can be useful to be able to draw these circles around triangles for problems. Because of this circle, the circumcenter is the same distance from each of the vertices because they are all on radii of the circle.[br][br]When the triangle is acute, the circumcenter is inside the triangle, when the triangle is right the circumcenter is on the triangle, and when the triangle is obtuse the circumcenter is outside the triangle.[br][br]The circle you drew is the circumcircle, you should see that it touches A, B, and C regardless of how you manipulate the triangle.