Nine-point circle
Nine-point circle
Tetsuo Ida
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 16:10:08.
Nine-point circle
Nine-point circle
The nine-point circle is a circle that can be constructed by the nine concyclic points defined from the triangle. These nine points are :
1
.The midpoint of each side of the triangle.
2
.The foot of each altitude.
3
.The midpoint of the line segment from each vertex of the triangle to the orthocenter.
Construction
Construction
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EosSession["nine-point circle"];
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NewOrigami[10]
nine-point circle/Origami: Step 1
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NewPoint["E"{6,7}]
nine-point circle/Origami: Step 1
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triangle={Thick,Red,Line[{"A","E","B","A"}]};
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HO["E","A",Mark{{"EA","F1"},{"AB","F2"}}]!
nine-point circle/Origami: Step 3
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HO["A","B",Mark{{"AB","G1"},{"F1F2","O"}}]!
nine-point circle/Origami: Step 5
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HO["B","E",Mark{{"BE","H1"}}]!
nine-point circle/Origami: Step 7
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Point O is circumcenter
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circle1={Thick,Green,GraphicsCircle["O","OA"]};
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ShowOrigami[More{circle1,triangle}]
nine-point circle/Origami: Step 7
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HO["EA","B",Mark{{"EA","J1"}}]!
nine-point circle/Origami: Step 9
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HO["BA","E",Mark{{"BA","K1"},{"J1B","H"}}]!
nine-point circle/Origami: Step 11
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HO["EB","A",Mark{{"EB","L1"}}]!
nine-point circle/Origami: Step 13
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HO["A","H",Mark->{{"AH","M"}}]!
nine-point circle/Origami: Step 15
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HO["B","H",Mark->{{"BH","N"}}]!
nine-point circle/Origami: Step 17
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HO["E","H",Mark->{{"EH","P"}}]!
nine-point circle/Origami: Step 19
Verification
Verification