Image:Excircles.png
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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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