Excenter
Excenter
Load Eos
Load Eos
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<<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 14:36:41.
Excenter
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.
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EosSession["Excenter"];
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NewOrigami[8,MarkPoints{"A0","B0","C0","D0"}]
Excenter: Step 1
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NewPoint[{"E"{4,7.2},"A"{3,4},"B"{6.5,4}}]
Excenter: Step 1
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triangle={Red,Thick,Line[{"E","A","B","E"}]};
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ShowOrigami[Moretriangle]
Excenter: Step 1
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HO["AE",Mark{{"A0B0","E0"}}]!
Excenter: Step 3
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HO["AE","AB"]
Excenter: Step 3
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,
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HO["AE","AB",FoldLine2,Mark{{"A0B0","F"}}]!
Excenter: Step 5
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HO["BE",Mark{{"C0B0","G"}}]!
Excenter: Step 7
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HO["BA","BE"]
Excenter: Step 7
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,
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HO["BA","BE",FoldLine1,Mark{{"AF","I"}}]!
Excenter: Step 9
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HO["AE","BE"]
Excenter: Step 9
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,
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HO["AE","BE",FoldLine2]!
Excenter: Step 11
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HO["E0E","I",Mark{{"E0E","E1"}}]!
Excenter: Step 13
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HO["EG","I",Mark{{"EG","G1"}}]!
Excenter: Step 15
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