The circles of a triangle

A movable triangle and some associated circles, showing

- The perpindicular bisector of each edge (blue). Cuts each edge in two.
- The angle bisector of each angle (purple). Cuts each angle in two.
- The circumcircle (dashed blue). The smallest circle which contains the triangle.
- The incircle (dashed purple). The largest circle contained inside the triangle.
- The Centroid (green). Intersection of lines joining center to midpoint of opposite edges. (off by default)
- The Orthocenter (cyan). Intersection of altitudes, lines perpendicular to each edge through the vertices. (off by default)

Drag the points A, B and C about to see the how things change.

Draw:

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 circumcircle. Equlatrial and isosceles triangles have other notable properties.

If you want to play with the code you can clone the fiddle page.

**Alex Gian**
Thu Jul 4 2024

Nice. Although you could probably add that the centroid, the circumcentre and and the orthocenter are colinear, lying on what is called the Euler line.