# Circumcenter

Circumcenter

## Load Eos

Load Eos

<<"EosHeader.m"

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g3 Version 1.2.9

Eos3.31 (November 5,2020) running under Mathematica 12.1.1 for Mac OS X x86 (64-bit) (June 22, 2020)

## 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.

EosSession["Circumcenter"];

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MarkOn[];

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NewOrigami[10]

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Circumcenter: Step 1

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NewPoint["E"{7,8}]

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Circumcenter: Step 1

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HO["A","E"]!

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Circumcenter: Step 3

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

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Circumcenter: Step 5

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HO["A","B"]!

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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}]

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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}}]

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Proof is successful.

Circumcenter: Step 7

Success,0.070567,

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EndSession[];

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