Incenter
Incenter
Load Eos
Load Eos
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<<EosLoader`
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 16:17:38.
Incenter
Incenter
For any triangle ΔABE, the angle bisectors of the three angles ∡A, ∡B and ∡E meet at the same point I.
Point I is the incenter of ΔABE.
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EosSession["Incenter"];
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NewOrigami[10]
Incenter/Origami: Step 1
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NewPoint["E"{9,8}]
Incenter/Origami: Step 1
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HO["AE"]!
Incenter/Origami: Step 3
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HO["AE","AB"]
Incenter/Origami: Step 3
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,
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HO["AE","AB",FoldLine1]!
Incenter/Origami: Step 5
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HO["BE"]!
Incenter/Origami: Step 7
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HO["BA","BE"]
Incenter/Origami: Step 7
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,
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HO["BA","BE",FoldLine2,Mark{{$fline[4],"I"}}]!
Incenter/Origami: Step 9
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HO["AB","I",Mark{{"AB","F"}}]!;
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triangle={Thick,Red,Line[{"A","B","E","A"}]};
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circle={Thick,Green,GraphicsCircle["I","IF"]};
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ShowOrigami[More{triangle,circle}]
Incenter/Origami: Step 11
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(*proofworksfromtheversionEos3.3.1*)
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Goal[O3Q["EA","EB","EI"]SquaredDistance["I","F"]==SquaredDistanceLine["I","EB"]==SquaredDistanceLine["I","EA"]SquaredDistanceLine["I","AB"]];
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Prove["Incenter",Mapping{"A"{0,0},"B"{1,0},(*"C"{1,1},"D"{0,1},*)"E"{u,v}}]
Proof is successful.
Incenter/Origami: Step 11
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EndSession[];