Construction in GCLC language

dim 120 120

point H 80 72.73
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_rt H
cmark_b H_{a}
color 0 0 0
fontsize 10


% point E_{a} is given by the problem setting, but it has to belong to the line h_{a} which is constructible from the others objects given 
% DET:  points H and H_{a} are not the same
% Constructing a line h_{a} which passes through point H and point H_{a}
line h_{a} H H_{a} 

color 200 200 200
drawline h_{a}
color 0 0 0




% Constructing a point E_{a} such that HE_{a}/HH_{a}=0.5885094349067814
towards E_{a} H H_{a} 0.5885094349067814 
color 220 0 0
fontsize 11
cmark_r E_{a}
color 0 0 0
fontsize 10

color 200 200 200
drawsegment H H_{a} 
color 0 0 0



% Constructing a point A such that E_{a}A/E_{a}H=-1
towards A E_{a} H -1 
cmark_t A
color 200 200 200
drawsegment H A 
color 0 0 0


% NDG:  points H and E_{a} are not the same
% Constructing a circle k(E_{a},A) whose center is at point E_{a} and which passes through point H
circle k(E_{a},A) E_{a} H 

color 200 200 200
drawcircle k(E_{a},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 point P_{\_G61501} with coordinates (10,30)
point P_{\_G61501} 10 30 
cmark_r P_{\_G61501}

% Constructing a line L_{\_G61504} which passes through point E_{a} and point H_{a}
line L_{\_G61504} E_{a} H_{a} 

color 200 200 200
drawline L_{\_G61504}
color 0 0 0


% Constructing a line L_{\_G61507} which is perpendicular to line L_{\_G61504} and which passes through point H_{a}
perp L_{\_G61507} H_{a} L_{\_G61504} 

color 200 200 200
drawline L_{\_G61507}
color 0 0 0


% Constructing a line L_{\_G61510} which passes through point E_{a} and point P_{\_G61501}
line L_{\_G61510} E_{a} P_{\_G61501} 

color 200 200 200
drawline L_{\_G61510}
color 0 0 0


% Constructing a point B which belongs to line L_{\_G61510} and line L_{\_G61507}
intersec B L_{\_G61510} L_{\_G61507} 
cmark_b B


% DET:  points B and H are not the same
% Constructing a line h_{b} which passes through point B and point H
line h_{b} B H 

color 200 200 200
drawline h_{b}
color 0 0 0



% NDG:  line h_{b} and circle k(E_{a},A) intersect% DET:  points H and H_{b} must be different
% Constructing a point P_{\_G61911} which is a foot of the point E_{a} on the line h_{b}
foot P_{\_G61911} E_{a} h_{b} 
cmark_r P_{\_G61911}
color 200 200 200
drawline E_{a} P_{\_G61911} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point H in the symmetry to point/line P_{\_G61911}
sim H_{b} P_{\_G61911} H 
cmark_rt H_{b}


% DET:  points A and H_{b} are not the same
% Constructing a line b which passes through point A and point H_{b}
line b A H_{b} 

color 200 200 200
drawline b
color 0 0 0



% NDG:  lines a and b are not parallel% DET:  lines a and b are not the same
% Constructing a point C which belongs to line a and line b
intersec C a b 
cmark_b C



drawsegment A B
drawsegment A C
drawsegment B C

% Non-degenerate conditions:  lines a and b are not parallel; line h_{b} and circle k(E_{a},A) intersect; points H and E_{a} are not the same
% Determination conditions:  lines a and b are not the same; points A and H_{b} are not the same; points H and H_{b} must be different; points B and H are not the same; points H and H_{a} are not the same