A movable triangle and some associated circles, showing
Drag the points A, B and C about to see the how things change.
A few points to note. The three perpindicular bisectors intersect at the center of the excircles. The three angle bisectors intersect at the center of the incircle. Each perpindicular bisectors intersects with and anglebisector at a point on the excircle. Equlatrial and isosceles triangles have other notable properties.
If you want to play with the code you can clone the fiddle page.