Some articles on point, points, point circle, circles:
Points, Lines, and Circles Associated With A Triangle
... There are hundreds of different constructions that find a special point associated with (and often inside) a triangle, satisfying some unique property see the references section for a ... with the three sides (or vertices) and then proving that the three lines meet in a single point an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for ... associated with a triangle are often constructed by proving that three symmetrically constructed points are collinear here Menelaus' theorem gives a useful general criterion ...
... There are hundreds of different constructions that find a special point associated with (and often inside) a triangle, satisfying some unique property see the references section for a ... with the three sides (or vertices) and then proving that the three lines meet in a single point an important tool for proving the existence of these is Ceva's theorem, which gives a criterion for ... associated with a triangle are often constructed by proving that three symmetrically constructed points are collinear here Menelaus' theorem gives a useful general criterion ...
Other Properties of The Nine-point Circle
... The radius of a triangle's circumcircle is twice the radius of that triangle's nine-point circle ... Figure 3 A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle ... Figure 4 The center of any nine-point circle (the nine-point center) lies on the corresponding triangle's Euler line, at the midpoint between that triangle's orthocenter and circumcenter ...
... The radius of a triangle's circumcircle is twice the radius of that triangle's nine-point circle ... Figure 3 A nine-point circle bisects a line segment going from the corresponding triangle's orthocenter to any point on its circumcircle ... Figure 4 The center of any nine-point circle (the nine-point center) lies on the corresponding triangle's Euler line, at the midpoint between that triangle's orthocenter and circumcenter ...
Nine-point Hyperbola
... The nine-point hyperbola was first discovered by E.F ... to take the work that English Mathematician Frank Morley completed on the nine-point circle using complex numbers in his book Inverse Geometry (1933) and apply it ... The nine-point hyperbola was recalled by Isaak Yaglom when describing Minkowskian geometry in the conclusion of his book A Simple Non-Euclidean Geometry and its Physical Basis (1979) ...
... The nine-point hyperbola was first discovered by E.F ... to take the work that English Mathematician Frank Morley completed on the nine-point circle using complex numbers in his book Inverse Geometry (1933) and apply it ... The nine-point hyperbola was recalled by Isaak Yaglom when describing Minkowskian geometry in the conclusion of his book A Simple Non-Euclidean Geometry and its Physical Basis (1979) ...
Orthocentric System - Further Properties
... pair of the original four orthocentric points will produce pairs of connectors that are orthogonal to each other such that they satisfy the distance equations where R is the common circumradius of the four possible ... sines result in the identity Feuerbach's theorem states that the nine-point circle is tangent to the incircle and the three excircles of a reference triangle ... Because the nine-point circle is common to all four possible triangles in an orthocentric system it is tangent to 16 circles comprising the incircles and excircles of ...
... pair of the original four orthocentric points will produce pairs of connectors that are orthogonal to each other such that they satisfy the distance equations where R is the common circumradius of the four possible ... sines result in the identity Feuerbach's theorem states that the nine-point circle is tangent to the incircle and the three excircles of a reference triangle ... Because the nine-point circle is common to all four possible triangles in an orthocentric system it is tangent to 16 circles comprising the incircles and excircles of ...
Famous quotes containing the words circle and/or point:
“Men go out to admire the heights of mountains, the huge waves of the sea, the broadest spans of rivers, the circle of ocean, the revolutions of stars, and leave themselves behind.”
—St. Augustine (354–430)
“Consider a man riding a bicycle. Whoever he is, we can say three things about him. We know he got on the bicycle and started to move. We know that at some point he will stop and get off. Most important of all, we know that if at any point between the beginning and the end of his journey he stops moving and does not get off the bicycle he will fall off it. That is a metaphor for the journey through life of any living thing, and I think of any society of living things.”
—William Golding (b. 1911)
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