Category:Circle of Apollonius is Circle

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This category contains pages concerning Circle of Apollonius is Circle:


Let $A, B$ be distinct points in the plane.

Let $\lambda \in \R_{>0}$ be a strictly positive real number.


Let $X$ be the locus of points in the plane such that:

$XA = \lambda \paren {XB}$


Then $X$ is in the form of a circle, known as a circle of Apollonius.


Circle-of-Apollonius.png


If $\lambda < 1$, then $A$ is inside the circle, and $B$ is outside.

If $\lambda > 1$, then $B$ is inside the circle, and $A$ is outside.

Pages in category "Circle of Apollonius is Circle"

The following 3 pages are in this category, out of 3 total.