Abstract
This paper describes the geometric meaning of the inner product of 2 circles based on Compass Ruler Algebra, the Conformal Geometric Algebra in 2D. It analyzes in detail the cases of intersecting and tangent circles as well as when one circle is completely inside or completely outside the other circle. The paper reflects the systematic way of deriving the results based on the Geometric Algebra software tool Gaalop. The results are easily conferrable to arbitrary dimensions.
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