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X₃₉₆₉¶

X₂₃₀₈com[INVERSE(n(INCENTRAL TRIANGLE))]

X₃₉₆₉ (X₂₃₀₈com[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_3969 = X_2308com[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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03969(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3969 = X_2308com[INVERSE(n(INCENTRAL TRIANGLE))] on reference triangle ABC."""
            X_3969 = eval_barycentric_point(model, A, B, C, '((b + c)*(b**(2) + c**(2) - a**(2) + b*c))', ID="X_3969", classes=["selected", "target"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            X_199 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) - a**(4) + (b**(2) + c**(2) - a**(2))*(b*c + c*a + a*b)))', ID="X_199", classes=["center", "incident"])
            central_line(model, X_100, X_199, 100, 199, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_405 = eval_trilinear_point(model, A, B, C, 'b*c*(a + b + c) + a*b*c*cos(A)', ID="X_405", classes=["center", "incident"])
            central_line(model, X_8, X_405, 8, 405, incident=True)
            X_226 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cos(B) + cos(C))', ID="X_226", classes=["center", "incident"])
            X_306 = eval_trilinear_point(model, A, B, C, '(b**(2)*c**(2))*(b + c)*cos(A)', ID="X_306", classes=["center", "incident"])
            central_line(model, X_226, X_306, 226, 306, incident=True)
            return promote_point_to_top(model, X_3969)


        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_3969 on the given reference triangle."""
            model = create_model('X_3969 = X_2308com[INVERSE(n(INCENTRAL TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03969(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-03969.json"))
            write_center_svg(
                model_acute,
                here / "x-03969.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3969¶

X₃₉₆₉¶