Excenter

Load Eos

<<"EosHeader.m"
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Excenter

For any triangle ΔABE, the angle bisectors of the three angles ∡E, π-∡A and π-∡B meet at the same point I.
Point I is called the excenter of ΔEAB.
EosSession["Excenter"];
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NewOrigami[8,MarkPoints{"A0","B0","C0","D0"}]
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Excenter: Step 1
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NewPoint[{"E"{4,7.2},"A"{3,4},"B"{6.5,4}}]
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Excenter: Step 1
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triangle={Red,Thick,Line[{"E","A","B","E"}]};
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ShowOrigami[Moretriangle]
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Excenter: Step 1
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HO["AE",Mark{{"A0B0","E0"}}]!
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Excenter: Step 3
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HO["AE","AB"]
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Excenter: Step 3

,

Out[]=
HO["AE","AB",FoldLine2,Mark{{"A0B0","F"}}]!
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Excenter: Step 5
Out[]=
HO["BE",Mark{{"C0B0","G"}}]!
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Excenter: Step 7
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HO["BA","BE"]
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Excenter: Step 7

,

Out[]=
HO["BA","BE",FoldLine1,Mark{{"AF","I"}}]!
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Excenter: Step 9
Out[]=
HO["AE","BE"]
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Excenter: Step 9

,

Out[]=
HO["AE","BE",FoldLine2]!
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Excenter: Step 11
Out[]=
HO["E0E","I",Mark{{"E0E","E1"}}]!
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Excenter: Step 13
Out[]=
HO["EG","I",Mark{{"EG","G1"}}]!
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