Construction in GCLC language

dim 120 120

point E_{c} 95 56.36
point H_{a} 80 40

color 220 0 0
fontsize 11

cmark_r E_{c}
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 circle k(E_{c},C) which is constructible from the others objects given 
% NDG:  points H_{a} and E_{c} are not the same
% Constructing a circle k(E_{c},C) whose center is at point E_{c} and which passes through point H_{a}
circle k(E_{c},C) E_{c} H_{a} 

color 200 200 200
drawcircle k(E_{c},C)
color 0 0 0




% Generating number V[_G20073] with value 0.8862654504542705
number V[_G20073] 0.8862654504542705 


% Calculating value V[_G20094] using formula V[_G20073]*360
expression V[_G20094]  { V[_G20073]*360  } 


% Constructing a point C which is an image of the point V[_G20094] in a rotation around the point E_{c} for the angle H_{a}
rotate C E_{c} V[_G20094] H_{a} 
color 220 0 0
fontsize 11
cmark_b C
color 0 0 0
fontsize 10

color 200 200 200
drawarc_p E_{c} H_{a} V[_G20094] 
color 0 0 0



% Constructing a point H such that CH/CE_{c}=2
towards H C E_{c} 2 
cmark_rt H
color 200 200 200
drawsegment C H 
color 0 0 0


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

color 200 200 200
drawline a
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 point A such that H_{a}A/H_{a}H=0.8862654504542705
towards A H_{a} H 0.8862654504542705 
cmark_t A
color 200 200 200
drawsegment H_{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:  line b and circle k(E_{c},C) intersect% DET:  points C and H_{b} must be different
% Constructing a point P_{\_G20651} which is a foot of the point E_{c} on the line b
foot P_{\_G20651} E_{c} b 
cmark_r P_{\_G20651}
color 200 200 200
drawline E_{c} P_{\_G20651} 
color 0 0 0

% Constructing a point H_{b} which is an image of the point C in the symmetry to point/line P_{\_G20651}
sim H_{b} P_{\_G20651} C 
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_{c},C) intersect; points H_{a} and E_{c} 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 C and H_{b} must be different; points A and C are not the same; points H_{a} and H are not the same; points C and H_{a} are not the same