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X₃₉₉₅¶

X₇₅₆com[INVERSE(n(INCENTRAL TRIANGLE))]

X₃₉₉₅ = homothetic center of anticomplementary triangle and inverse of n(Medial)*n(Incentral) triangle

X₃₉₉₅ (X₇₅₆com[INVERSE(n(INCENTRAL TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3995 = X_756com[INVERSE(n(INCENTRAL TRIANGLE))]."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03995(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3995 = X_756com[INVERSE(n(INCENTRAL TRIANGLE))] on reference triangle ABC."""
            X_3995 = eval_barycentric_point(model, A, B, C, '((b + c)*(a**(2) + a*b + a*c - b*c))', ID="X_3995", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_2, X_37, 2, 37, incident=True)
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            central_line(model, X_72, X_145, 72, 145, incident=True)
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center", "incident"])
            X_190 = eval_trilinear_point(model, A, B, C, 'b*c/(b - c)', ID="X_190", classes=["center", "incident"])
            central_line(model, X_81, X_190, 81, 190, incident=True)
            return promote_point_to_top(model, X_3995)


        def build_model(
            sides: tuple[float, float, float] = (5.0, 6.0, 7.0),
            show_guides: bool = False,
        ) -> Model:
            """Build a `geometor.model.Model` for X_3995 on the given reference triangle."""
            model = create_model('X_3995 = X_756com[INVERSE(n(INCENTRAL TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03995(model, A, B, C)
            return model


        if __name__ == "__main__":
            here = Path(__file__).resolve().parent
            model_acute = build_model((5.0, 6.0, 7.0))
            model_acute.save(str(here / "x-03995.json"))
            write_center_svg(
                model_acute,
                here / "x-03995.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3995¶

X₃₉₉₅¶