Construction in GCLC language
dim 120 120
point O 65 51.14
point G 70 58.33
point H_{a} 80 40
color 220 0 0
fontsize 11
cmark_t O
cmark_t G
cmark_b H_{a}
color 0 0 0
fontsize 10
% Constructing a point H such that OH/OG=3
towards H O G 3
cmark_rt H
color 200 200 200
drawsegment O H
color 0 0 0
% DET: points H_{a} and H are not the same
% Constructing a line h_{a} which passes through point H_{a} and point H
line h_{a} H_{a} H
color 200 200 200
drawline h_{a}
color 0 0 0
% Constructing a line a which is perpendicular to line h_{a} and which passes through point H_{a}
perp a H_{a} h_{a}
color 200 200 200
drawline a
color 0 0 0
% Constructing a line m_{a} which is perpendicular to line a and which passes through point O
perp m_{a} O a
color 200 200 200
drawline m_{a}
color 0 0 0
% NDG: lines m_{a} and a are not parallel% DET: lines m_{a} and a are not the same
% Constructing a point M_{a} which belongs to line m_{a} and line a
intersec M_{a} m_{a} a
cmark_b M_{a}
% Constructing a point A such that M_{a}A/M_{a}G=3
towards A M_{a} G 3
cmark_t A
color 200 200 200
drawsegment M_{a} A
color 0 0 0
% NDG: points A and O are not the same
% Constructing a circle k(O,C) whose center is at point O and which passes through point A
circle k(O,C) O A
color 200 200 200
drawcircle k(O,C)
color 0 0 0
% NDG: line a and circle k(O,C) intersect
% Constructing points C and B which are in intersection of k(O,C) and a
intersec2 C B k(O,C) a
cmark_b C
cmark_b B
drawsegment A B
drawsegment A C
drawsegment B C
% Non-degenerate conditions: line a and circle k(O,C) intersect; points A and O are not the same; lines m_{a} and a are not parallel
% Determination conditions: lines m_{a} and a are not the same; points H_{a} and H are not the same