## Special lines in a triangle

If the coordinates of the three vertices of a triangle are entered, the program calculates the equations of the perpendicular bisectors[1], of the side bisectors[2], of the angle bisectors[3] and of the altitudes[4]. In addition, the centers and radii of the circumcircle[5], of the incircle[6] and of the three excircles[7].

A list of check boxes can be used to select which objects are to be calculated and drawn.

Perpendicular bisec.
Medians
Angle bisectors
Altitudes
Incircle
Circumcircle
Excircles

### Example 1: incircle and excircles of a triangle

```Given:
¯¯¯¯¯¯
Vertices:    A(1|0)   B(5|1)   C(3|6)

Results:
¯¯¯¯¯¯¯
Sides:   a :  5·x + 2·y = 27
b :  3·x - y = 3
c :  x - 4·y = 1

Incircle:    Mi(3,119|1,962)         r i = 1,390

Excircles: Ma(7,626|6,136)       ra = 4,346
Mb(-4,356|5,784)      rb = 6,910
Mc(3,248|-2,427)      rc = 2,900```

The center of the incircle (green) lies on the bisector of the three interior angles. The centers of the excircles (red) are each on the bisector of an inner angle and on the bisector of the outside angle of the other two triangle angles. These construction lines are also drawn.

### Example 2: Altitudes in an obtuse-angled triangle

```Given:
¯¯¯¯¯¯
Vertices:  A(7|3)   B(16|10)  C(8|9)

Results:
¯¯¯¯¯¯¯
Sides:   a : -x + 8·y = 64
b : 6·x - y = 39
c : 7·x - 9·y = 22

Altitudes:  ha : 8·x + y = 59
hb : x + 6·y = 76
hc : 9·x + 7·y = 135

Perp. feet: Ha(6,277|8,785)  Hb(8,378|11,27)
Hc(10,53|5,746

Orthocenter: H(11,05|8,26)```

The intersection of the altitudes of an obtuse-angled triangle lies outside the triangle. The construction lines are also drawn. In order to make them more visible, the grid lines have been hidden.