## Solution of the Special Case "CLP" of the Problem of Apollonius via Vector Rotations using Geometric Algebra

**Authors:** James A. Smith

NOTE: A new Appendix presents alternative solutions.
The famous "Problem of Apollonius", in plane geometry, is to construct all of the circles that are tangent, simultaneously, to three given circles. In one variant of that problem, one of the circles has innite radius (i.e., it's a line). The Wikipedia article that's current as of this writing has an extensive description of the problem's history, and of methods that have been used to solve it. As described in that article, one of the methods reduces the "two circles and a line" variant to the so-called "Circle-Line-Point" (CLP) special case: Given a circle C, a line L, and a point P, construct the circles that are tangent to C and L, and pass through P. This document has been prepared for two very different audiences: for my fellow students of GA, and for experts who are preparing materials for us, and need to know which GA concepts we understand and apply readily, and which ones we do not.

**Comments:** 22 Pages.

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### Submission history

[v1] 2016-05-31 21:49:03

[v2] 2016-08-20 22:58:10

**Unique-IP document downloads:** 43 times

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