"A Triangle's Magic Circles" is a fun book that allows readers to discover the magic of GEOMETRY. The book is adapted to be understood by children from middle school and up, with hands-on practice in geometry. Such applications sharpen skills in observation, comparison, and logic. This book covers the concepts of cyclic quadrilateral, Thales' theorem, incircle construction, finding the orthocenter, and positioning of orthocenter, circumcenter, centroid and incenter. Finally, finding the properties of the Simpson Line, finding the nine-point circle center, the properties of the Euler Line, and those of the incenter. Geometry is, with arithmetic, one of the oldest branches of mathematics. It deals with properties of space that are related to distance, shape, size, and relative position of figures. Based on Euclidean geometry, it introduces the intuitive notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. Often developed with the aim to model the physical world, geometry has applications to almost all sciences, and to art, architecture, and other activities that are related to graphics.
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