Special Lines and Circles in a Triangle
The vertices of the drawn triangle can be moved with pressed mouse button.
The following lines and circles are displayed on request:
- Perpendicular bisectors:
Lines which meet the sides at their midpoints perpendicularly
- Circumcircle:
Circle around the intersection of the perpendicular bisectors through the vertices of the triangle
- Angle bisectors:
Lines which divide the interior angles into two angles with equal measures
- Incircle:
Circle around the intersection of the angle bisectors which touches the sides
- Exterior angle bisectors
- Excircles:
Circles, each touching one side and the extensions of the other two sides; the center of an excircle is the intersection
of the bisectors of one interior angle and two exterior angles.
- Midparallels:
Segments between the midpoints of the sides
- Medians:
Segments between the vertices and the midpoints of the opposite sides
- Centroid:
Intersection of the medians which are divided in the ratio 2:1
- Altitudes:
Segments (lines) through the vertices which are perpendicular to the opposite sides
Additionally for "professionals":
- Euler line:
Line which passes through circumcenter, centroid, and orthocenter (intersection of the altitudes); the centroid divides
the segment between orthocenter and circumcenter in the ratio 2:1.
- Nine-point circle (Feuerbach circle):
Circle around the midpoint of circumcenter and orthocenter which passes through the midpoints of the sides, the feet of the altitudes,
and the points halfway between the orthocenter and the vertices; the nine-point circle touches the incircle
and the three excircles; its radius is half the radius of the circumcircle.
Another small tip: If you select all fields at the same time, you will probably lose the overview. Less is more in this case!