# Orthocenter

Orthocenter

## Load Eos

Load Eos

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<<"EosHeader.m"

## Orthocenter

Orthocenter

The three (possibly extended) altitudes intersect in a single point H of the triangle. The point H is called the orthocenter of the triangle.

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EosSession["Orthocenter"];

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NewOrigami[10]

Orthocenter: Step 1

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NewPoint["E"{6,7}]

Orthocenter: Step 1

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HO["AE"]!

Orthocenter: Step 3

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HO["AE","B",Mark{"AE"}]!

Orthocenter: Step 5

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HO["BE"]!

Orthocenter: Step 7

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HO["BE","A",Mark{{"FB","H"}}]!

Orthocenter: Step 9

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Goal[O4Q["AB","E","EH"]];

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Prove["Orthocenter",Mapping{"A"{0,0},"B"{1,0},(*"C"{1,1},"D"{0,1},*)"E"{u,v}}]

Proof is successful.

Orthocenter: Step 9

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Success,0.027695,

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HO["AB","H",Mark{"AB"}]!

Orthocenter: Step 11

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ShowOrigami[More{Thick,Red,Line[{"A","E","B","A"}]}]

Orthocenter: Step 11

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EndSession[];