Circumcenter

Here we have triangle ABC. You can move points A, B, and C however you would like.[br][br]D represents the midpoint of AB[br]E represents the midpoint of AC[br]F represents the midpoint of BC[br][br]Clicking on each Perpendicular Bisector checkbox in the top left will create the perpendicular bisector through the corresponding line. Upon clicking two or more of these, the intersection of the perpendicular bisectors (G) will show. Clicking all three will show that they all intersect at the same point. This point is called the [b]circumcenter[/b] of the triangle.[br][br]Select all checkboxes so that all perpendicular bisectors are showing and move points A, B and C.[br][br]Do all three perpendicular bisectors always intersect at one point, no matter the triangle?[br]Can the circumcenter ever be outside of the triangle?

Information: Circumcenter