# Circumcenter

Circumcenter

## Load Eos

Load Eos

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<<EosLoader.m

Eos3.7.2 (June 24,2023) running under Mathematica 13.2.1 for Mac OS X ARM (64-bit) (January 27, 2023) on Fri 23 Jun 2023 16:01:48.

## 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.

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EosSession["Circumcenter"];

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MarkOn[];

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NewOrigami[10]

Circumcenter/Origami: Step 1

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NewPoint["E"{7,8}]

Circumcenter/Origami: Step 1

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HO["A","E"]!

Circumcenter/Origami: Step 3

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HO["B","E",Mark{{"FG","H"},{"BC","I"}}]!

Circumcenter/Origami: Step 5

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HO["A","B"]!

Circumcenter/Origami: 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/Origami: 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}}]

Proof is successful.

Circumcenter/Origami: Step 7

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EndSession[];