### 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

... 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-

... The radius of a triangle's circumcircle is twice the radius of that triangle's 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 ...Nine-point Hyperbola

... The nine-

... 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

... 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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