From TheBestLinks.com
A triangle with its incircle, excircles and angle bisectors. In the public domain. Created with GCLC using the following source code:
% The three vertices of the triangle
point A 25 70
point B 20 55
point C 45 60
% They define three lines
line a B C
line b A C
line c A B
% The three internal angle bisectors
bis bis_A B A C
bis bis_B A B C
bis bis_C B C A
% The three external angle bisectors
% They are perpendicular to the internal ones
perp extbis_A A bis_A
perp extbis_B B bis_B
perp extbis_C C bis_C
% The centers of the in- and excircles
intersec incenter bis_A bis_B
intersec a_excenter bis_A extbis_B
intersec b_excenter bis_B extbis_C
intersec c_excenter bis_C extbis_A
% The incircle.
% Find a point on the incircle
% by going perpendicular from the incenter
% to b (for instance).
perp dummy_line incenter b
intersec touch dummy_line b
circle incircle incenter touch
% The excircles.
perp dummy_line a_excenter a
intersec touch dummy_line a
circle a_excircle a_excenter touch
perp dummy_line b_excenter b
intersec touch dummy_line b
circle b_excircle b_excenter touch
perp dummy_line c_excenter c
intersec touch dummy_line c
circle c_excircle c_excenter touch
% Now draw everything
dim 70 100
color 0 200 0
drawline extbis_A
drawline extbis_B
drawline extbis_C
color 255 0 0
drawline bis_A
drawline bis_B
drawline bis_C
linethickness 3
color 120 0 120
drawcircle incircle
color 0 0 240
drawcircle a_excircle
drawcircle b_excircle
drawcircle c_excircle
color 0 0 0
drawline a
drawline b
drawline c
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