If four points form an orthocentricsystem, then each of the four points is the orthocenter of the other three -- thus there are four possible triangles.

The mathematical object that goes by the name of complete quadrilateral is neither complete nor quadrilateral, at least not in the sense in which the word "quadrilateral" appears in, say, Brahmagupta's theorem about cyclic quadrilaterals.

A complete quadrilateral is a configuration of four straight lines in general position and six points at which the lines intersect.

Morley, Orthocentric Properties of the Plane n-Line, Trans Amer Math Soc, 4 (1903) 1-12.

If an orthocentricsystem of four points is given, then the four triangles formed by any combination of three distinct points of that system all have the same nine point circle.

Orthocentric system Definition / Orthocentric system Research(Site not responding. Last check: )

In geometry, an orthocentricsystem is a set of four points in the plane where one point is the orthocenterIn geometry, an altitude of a triangle is a straight line through a vertex and perpendicular to (i.e.

The orthocentric portion 26 is the most prominent of the three portions and corresponds to the apex of a chamber which encloses the pad 38.

Thus, the orthocentric portion 26 is the bulkiest and thickest portion of the sanitary napkin 12, located precisely in the orthocenter of the napkin between the other two portions 28 and 30, with which the orthocentric portion defines an indivisible and uniform body.

The orthocentric portion 26, the most prominent part of the sanitary napkin 12, must be adjusted to the area around the vaginal orifice, with the narrow portion 30 oriented towards the back.

In an orthocentricsystem, each point is the orthocenter of the triangle of the other three, as illustrated above (Coxeter and Greitzer 1967, p.

The incenter and excenters of a triangle are an orthocentricsystem.

The centers of the circumcircles of the points in an orthocentricsystem form another orthocentricsystem congruent to the first, and are the reflection of the original points in their common nine-point...

The orthocenter lies inside the triangle if and only if the triangle is not obtuse.\nThe three vertices together with the orthocenter are said to form an orthocentricsystem.

An angle bisector of a triangle is a straight line through a vertex which cuts the corresponding angle in half.

The four points A, B, C and H taken three at a time form four triangles - ABC, ABH, BCH, CAH - with the property that the remaining point serves as the orthocenter of the corresponding triangle.

The incenter of a triangle together with its three excenters form the configuration of four points that fits the foregoing discussion.

In particular, the excenters and the incenter of a triangle form an orthocentricsystem.

Orthocentric system -- Facts, Info, and Encyclopedia article(Site not responding. Last check: )

In (The pure mathematics of points and lines and curves and surfaces) geometry, an orthocentricsystem is a set of four points in the plane where one point is the (Click link for more info and facts about orthocenter) orthocenter of the (A three-sided polygon) triangle formed by the other three.

The centers of the (Click link for more info and facts about incircle) incircle and (Click link for more info and facts about excircle) excircles of a triangle form an orthocentricsystem.

CDC 6600 bei eLexi - das Onlinelexikon(Site not responding. Last check: )

The basis for the 6600 is what we would today refer to as a RISC system, one in which the processor is tuned to do instructions which are comparatively simple.

The philosophy of many other machines was toward using instructions which were complicated — for example, which would fetch an operand from memory and add it to a value in a register.

These machines, called peripheral processors, or PPUs, were full computers in their own right, but tuned to performing I/O tasks and running the operating system.

"Note_: As a matter of historical interest our readers may be reminded that the term ``Orthocentre'' was invented by two mathematicians, Besant and Ferrers, in 1865, while out for a walk along the Trumpington Road, a road leading out of Cambridge toward London.

A tetrahedron with this property is called an orthocentric tetrahedron.

It is known that if three altitudes of a tetrahedron are concurrent, the fourth will also pass through the same point.

See all pages with references to "orthocentricsystem".

40 An orthocentricsystem consists of four points,...

Since the incenter and the excenters form an orthocentricsystem, each being the orthocenter of the triangle formed by the others [2], it is known [7] that any conic passing...

wiki/Feuerbach point Definition / wiki/Feuerbach point Research(Site not responding. Last check: )

J, K, L - the points on each altitude midway between the vertex and the orthocentre (labelled S) The nine point circle is tangent externally to the three excirclesIn geometry, the incircle or inscribed circle of a triangle is the largest circle contained in the triangle; it touches (is tangent to) the three sides.

If an orthocentric systemIn geometry, an orthocentricsystem is a set of four points in the plane where one point is the orthocenter of the triangle formed by the other three.

An orthocentricsystem is given by the picture below and here on GSP.

Itâ€™s simply the four sets of triangles given by one triangle A, B, C and its orthocenter, H. According to this picture there are four such different combinations, and all of their circumcircles have an equal radius.

So our assumption that all the circumcircles in our orthocentricsystem are the same is true.