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application bisector boundary point center of inversion Chapter circle of inversion circular region collinear complete quadrangle concept congruent conic contains convex body convex hull convex set corresponding points definition determined distance distinct points elliptic geometry endpoints equations Euclidean geometry exactly example Exercises fifth postulate Find the image finite geometry fractal given line given point glide reflection group of transformations harmonic set homogeneous coordinates hyperbolic geometry ideal point interior point invariant inverse points isogonal conjugates length mapping mathematics measure midpoint motions nine-point circle non-Euclidean geometry omega triangle perpendicular perspective plane dual point of intersection problem Problem-Solving Idea projective geometry proof of Theorem properties Prove radius ratio real numbers Reuleaux triangle rotation Saccheri quadrilateral Section segment set of axioms set of points shown in Figure shows similar simple closed curve statement straight line straightedge supporting line symmedian tangent three points three-space topological translation vector vertex vertices