Construction in GCLC language

dim 120 120

point E_{a} 80 83.86
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_r E_{a}
cmark_b H_{a}
color 0 0 0
fontsize 10


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

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 point P_{\_G31153} with coordinates (10,30)
point P_{\_G31153} 10 30 
cmark_r P_{\_G31153}

% Constructing a line L_{\_G31156} which passes through point E_{a} and point H_{a}
line L_{\_G31156} E_{a} H_{a} 

color 200 200 200
drawline L_{\_G31156}
color 0 0 0


% Constructing a line L_{\_G31159} which is perpendicular to line L_{\_G31156} and which passes through point H_{a}
perp L_{\_G31159} H_{a} L_{\_G31156} 

color 200 200 200
drawline L_{\_G31159}
color 0 0 0


% Constructing a line L_{\_G31162} which passes through point E_{a} and point P_{\_G31153}
line L_{\_G31162} E_{a} P_{\_G31153} 

color 200 200 200
drawline L_{\_G31162}
color 0 0 0


% Constructing a point C which belongs to line L_{\_G31162} and line L_{\_G31159}
intersec C L_{\_G31162} L_{\_G31159} 
color 220 0 0
fontsize 11
cmark_b C
color 0 0 0
fontsize 10




% Constructing a point A such that E_{a}A/E_{a}H_{a}=0.8803890310922553
towards A E_{a} H_{a} 0.8803890310922553 
cmark_t A
color 200 200 200
drawsegment E_{a} H_{a} 
color 0 0 0



% Constructing a point H such that AH/AE_{a}=2
towards H A E_{a} 2 
cmark_rt H
color 200 200 200
drawsegment A H 
color 0 0 0


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

color 200 200 200
drawline b
color 0 0 0



% NDG:  points A 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 A
circle k(E_{a},A) E_{a} A 

color 200 200 200
drawcircle k(E_{a},A)
color 0 0 0



% NDG:  line b and circle k(E_{a},A) intersect% DET:  points A and H_{b} must be different
% Constructing a point P_{\_G31833} which is a foot of the point E_{a} on the line b
foot P_{\_G31833} E_{a} b 
cmark_r P_{\_G31833}
color 200 200 200
drawline E_{a} P_{\_G31833} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point A in the symmetry to point/line P_{\_G31833}
sim H_{b} P_{\_G31833} A 
cmark_rt H_{b}


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

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



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



drawsegment A B
drawsegment A C
drawsegment B C

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