Three Solutions to Apollonius Problem LLP Limiting Case

This worksheet enables students to explore the solution presented in the article "Three Solutions of the LLP Limiting Case of the Problem of Apollonius via Geometric Algebra, Using Reflections and Rotations" ( This resource is part of a series that I am preparing in support of Professor David Hestenes's goal of using Geometric Algebra(GA) to integrate high-school algebra,geometry, trigonometry,and physics into a coherent curriculum. Previous materials in this series: Dot Product: Geometric Significance and GeoGebra Coding ( Inner and Outer Products of Vectors Inscribed in a Circle ( Geometric Algebra: Find unknown vector from two dot products ( GeoGebra coding/usage of Geometric Algebra's wedge product ( Tangents to a circle from a point, using Geometric Algebra ( Apollonius Problem: Solution via Vectors (Geometric Algebra) ( Resources prepared by Professor Hestenes and Robert Rowley: LinkedIn group for collaborative development of pre-university materials on GA: Pre-University Geometric Algebra Wiki for the same purpose: