| 1. | Consequently, the other four points form an orthocentric system.
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| 2. | The incenter and excenters together form an orthocentric system.
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| 3. | In an orthocentric tetrahedron the four altitudes are Monge point of the tetrahedron.
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| 4. | The center of this common nine-point circle lies at the centroid of the four orthocentric points.
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| 5. | Note that the incenter of this common orthic triangle must be one of the original four orthocentric points.
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| 6. | Another necessary and sufficient condition for a tetrahedron to be orthocentric is that its three bimedians have equal length.
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| 7. | If all three pairs of opposite edges of a tetrahedron are perpendicular, then it is called an orthocentric tetrahedron.
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| 8. | The orthocentric point that becomes the incenter of the orthic triangle is that orthocentric point closest to the common nine-point center.
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| 9. | The orthocentric point that becomes the incenter of the orthic triangle is that orthocentric point closest to the common nine-point center.
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| 10. | When only one pair of opposite edges are perpendicular, it is called a "'semi-orthocentric tetrahedron " '.
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