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 B 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_{\_G11176} with coordinates (10,30)
point P_{\_G11176} 10 30 
cmark_r P_{\_G11176}

% Constructing a line L_{\_G11179} which passes through point E_{a} and point H_{a}
line L_{\_G11179} E_{a} H_{a} 

color 200 200 200
drawline L_{\_G11179}
color 0 0 0


% Constructing a line L_{\_G11182} which is perpendicular to line L_{\_G11179} and which passes through point H_{a}
perp L_{\_G11182} H_{a} L_{\_G11179} 

color 200 200 200
drawline L_{\_G11182}
color 0 0 0


% Constructing a line L_{\_G11185} which passes through point E_{a} and point P_{\_G11176}
line L_{\_G11185} E_{a} P_{\_G11176} 

color 200 200 200
drawline L_{\_G11185}
color 0 0 0


% Constructing a point B which belongs to line L_{\_G11185} and line L_{\_G11182}
intersec B L_{\_G11185} L_{\_G11182} 
color 220 0 0
fontsize 11
cmark_b B
color 0 0 0
fontsize 10




% Constructing a point A such that E_{a}A/E_{a}H_{a}=0.922968965433203
towards A E_{a} H_{a} 0.922968965433203 
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 B are not the same
% Constructing a line c which passes through point A and point B
line c A B 

color 200 200 200
drawline c
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 c and circle k(E_{a},A) intersect% DET:  points A and H_{c} must be different
% Constructing a point P_{\_G11856} which is a foot of the point E_{a} on the line c
foot P_{\_G11856} E_{a} c 
cmark_r P_{\_G11856}
color 200 200 200
drawline E_{a} P_{\_G11856} 
color 0 0 0

% Constructing a point H_{c} which is an image of the point A in the symmetry to point/line P_{\_G11856}
sim H_{c} P_{\_G11856} A 
cmark_lt H_{c}


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

color 200 200 200
drawline h_{c}
color 0 0 0



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



drawsegment A B
drawsegment A C
drawsegment B C

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