Radical Axis and Central Line
Except for the two special cases of a pencil of concentric circles and a pencil of coincident lines, any two circles within a pencil have the same radical axis, and all circles in the pencil have collinear centers. Any three or more circles from the same family are called coaxal circles or coaxial circles.
The elliptic pencil of circles passing through the two points C and D (the set of red circles, in the figure) has the line CD as its radical axis. The centers of the circles in this pencil lie on the perpendicular bisector of CD. The hyperbolic pencil defined by points C and D (the blue circles) has its radical axis on the perpendicular bisector of line CD, and all its circle centers on line CD.
The radical axis of any pencil of circles, interpreted as an infinite-radius circle, belongs to the pencil. Any three circles belong to a common pencil whenever all three pairs share the same radical axis and their centers are collinear.
Read more about this topic: Apollonian Circles
Famous quotes containing the words radical, axis, central and/or line:
“Our conscience is not the vessel of eternal verities. It grows with our social life, and a new social condition means a radical change in conscience.”
—Walter Lippmann (1889–1974)
“He is the essence that inquires.
He is the axis of the star;
He is the sparkle of the spar;
He is the heart of every creature;
He is the meaning of each feature;
And his mind is the sky,
Than all it holds more deep, more high.”
—Ralph Waldo Emerson (1803–1882)
“Incarnate devil in a talking snake,
The central plains of Asia in his garden,
In shaping-time the circle stung awake,
In shapes of sin forked out the bearded apple....”
—Dylan Thomas (1914–1953)
“The real dividing line between early childhood and middle childhood is not between the fifth year and the sixth year—it is more nearly when children are about seven or eight, moving on toward nine. Building the barrier at six has no psychological basis. It has come about only from the historic-economic-political fact that the age of six is when we provide schools for all.”
—James L. Hymes, Jr. (20th century)