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:
“What makes it so plausible to assume that hypocrisy is the vice of vices is that integrity can indeed exist under the cover of all other vices except this one. Only crime and the criminal, it is true, confront us with the perplexity of radical evil; but only the hypocrite is really rotten to the core.”
—Hannah Arendt (1906–1975)
“A book is not an autonomous entity: it is a relation, an axis of innumerable relations. One literature differs from another, be it earlier or later, not because of the texts but because of the way they are read: if I could read any page from the present time—this one, for instance—as it will be read in the year 2000, I would know what the literature of the year 2000 would be like.”
—Jorge Luis Borges (1899–1986)
“Friends serve central functions for children that parents do not, and they play a critical role in shaping children’s social skills and their sense of identity. . . . The difference between a child with close friendships and a child who wants to make friends but is unable to can be the difference between a child who is happy and a child who is distressed in one large area of life.”
—Zick Rubin (20th century)
“The middle years of parenthood are characterized by ambiguity. Our kids are no longer helpless, but neither are they independent. We are still active parents but we have more time now to concentrate on our personal needs. Our children’s world has expanded. It is not enclosed within a kind of magic dotted line drawn by us. Although we are still the most important adults in their lives, we are no longer the only significant adults.”
—Ruth Davidson Bell. Ourselves and Our Children, by Boston Women’s Health Book Collective, ch. 3 (1978)