Circumcenter
Circumcenter
Load Eos
Load Eos
In[]:=
<<EosLoader`
Eos3.7.1.1 (March 21,2023) running under Mathematica 13.2.0 for Mac OS X ARM (64-bit) (November 18, 2022) on Thu 30 Mar 2023 11:40:26.
Circumcenter
Circumcenter
For any triangle ΔABE, the perpendicular bisectors of the three edges AB, BE and EA meet at the same point H.
Point H is called the circumcenter of ΔABE.
In[]:=
EosSession["Circumcenter"];
In[]:=
MarkOn[];
In[]:=
NewOrigami[10]
Circumcenter: Step 1
Out[]=
In[]:=
NewPoint["E"{7,8}]
Circumcenter: Step 1
Out[]=
In[]:=
HO["A","E"]!
Circumcenter: Step 3
Out[]=
In[]:=
HO["B","E",Mark{{"FG","H"},{"BC","I"}}]!
Circumcenter: Step 5
Out[]=
In[]:=
HO["A","B"]!
Circumcenter: Step 7
Out[]=
In[]:=
circle={Thick,Green,GraphicsCircle["H","AH"]};triangle={Thick,Red,Line[{"A","B","E","A"}]};
In[]:=
ShowOrigami[More{circle,triangle}]
Circumcenter: Step 7
Out[]=
In[]:=
Prove["circumcenter",Goal(IncidentQ["H","JK"]∧SquaredDistance["H","A"]==SquaredDistance["H","B"]SquaredDistance["H","E"]),Mapping{"A"{0,0},"B"{1,0},"C"{1,1},"D"{0,1},"E"{u,v}}]
Proof is successful.
Circumcenter: Step 7
Out[]=
In[]:=
EndSession[];