Points of Intersection 17: Mirror Polygons and Incircle Intersections

This example demonstrates a geometric construction where a triangle is mirrored, incircles are drawn, and multiple intersection points are computed, incorporating natural numbers, combinatorics, and the tangent function. The core mathematical concepts include two-dimensional vectors, polygon reflection, incircle properties, intersection of lines and circles, and the geometric interpretation of the tangent function. The construction uses GeoGebra commands such as Polygon to create the initial triangle poly1, Mirror to generate the reflected triangle poly1', Incircle to construct incircles, and Intersect to find points D through P where sides, circles, and mirrored elements meet. Objects include A, B, C, poly1, c, a, b, A', B', C', poly1', c', a', b', D, E, F, G, H, I, d, inc_1, e, inc_2, f, inc, J, K, L, g, h, k, M, N, O, i, j, l, P. Suitable for high school and college students exploring geometric transformations, combinatorial patterns, and trigonometric functions, as well as for teachers demonstrating dynamic geometry constructions.