Vectors in Terms of Coordinates: Circumcircle and Incircle Decomposition

① This GeoGebra example demonstrates how to represent vectors using coordinates, integrating the circumcircle and incircle to illustrate the geometric meaning of vectors. ② Core mathematical concepts include coordinate representation of vectors, vector decomposition, the relationship between complex numbers and plane geometry, and properties of circumscribed and inscribed circles. ③ Construction highlights: the Intersect command is used to find intersection points, the Vector command constructs vectors, and objects A, B, P along with text1, text2, text3 display coordinate components or explanatory notes. ④ Suitable for high school or early college students learning analytic geometry, vector operations, and complex numbers, as well as for teachers demonstrating the combination of vectors and circles in class.