An Apollonius circle is the locus of the apex of a triangle on a given base, the other two sides of which are in a fixed ratio. Apollonius presented a construction for all of the other cases in Book I before completing the construction for the three circle case in Book II.

circle of Apollonius (plural circles of Apollonius). This term is especially used in mathematics subject where these axioms are of numerical logic with the systems in the form of the question. In this Demonstration, is the length of the base of the triangle and the ratio , where . http://demonstrations.wolfram.com/TheApolloniusCircleOfATriangle/ Apollonius’ theorem is a kind of theorem which relates to the length of the median of a triangle to the length of their sides. Named for the ancient Greek geometer and astronomer Apollonius of Perga (ca 262—ca 190 BCE).

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Construct a Triangle Given the Length of an Angle Bisector, the Angle at Another Vertex and the Distance from the Third Vertex to the Angle Bisector, The Plemelj Construction of a Triangle: 8, The Plemelj Construction of a Triangle: 7.

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