Circumcenter

Load Eos

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<<"EosHeader.m"

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.
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EosSession["Circumcenter"];
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MarkOn[];
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NewOrigami[10]
Circumcenter: Step 1
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NewPoint["E"{7,8}]
Circumcenter: Step 1
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HO["A","E"]!
Circumcenter: Step 3
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HO["B","E",Mark{{"FG","H"},{"BC","I"}}]!
Circumcenter: Step 5
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HO["A","B"]!
Circumcenter: Step 7
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circle={Thick,Green,GraphicsCircle["H","AH"]};​​triangle={Thick,Red,Line[{"A","B","E","A"}]};
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ShowOrigami[More{circle,triangle}]
Circumcenter: Step 7
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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}}]
ProofbyGB
::gbstart
:Proof by Groebner basis method started at March 22, 2021 at 10:50:40 PM JST.
ProofbyGB
::gbsuccess
:Proof by Groebner basis method is successful.CPU time used for Groebner basis computation is 0.056776 seconds.
Proof is successful.
Circumcenter: Step 7
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Success,0.056776,
circumcenter.nb

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EndSession[];