## Special lines in a triangle

If the coordinates of the three edges 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 should be calculated and drawn.

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

Given: ¯¯¯¯¯¯ Edges: A(1|0) B(5|1) C(3|6) Results: ¯¯¯¯¯¯¯ Vertices: 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 circles (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: ¯¯¯¯¯¯ Edges: A(7|3) B(16|10) C(8|9) Results: ¯¯¯¯¯¯¯ Vertices: 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.