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X₃₉₇₁¶

X₂com[INVERSE(n(INCENTRAL TRIANGLE))]

X₃₉₇₁ = incentral-to-ABC barycentric image of X₂

X₃₉₇₁ (X₂com[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_3971 = X_2com[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,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03971(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3971 = X_2com[INVERSE(n(INCENTRAL TRIANGLE))] on reference triangle ABC."""
            X_3971 = eval_barycentric_point(model, A, B, C, '(b + c)*(b*c - c*a - a*b)', ID="X_3971", classes=["selected", "target"])
            X_43 = eval_trilinear_point(model, A, B, C, 'a*b + a*c - b*c', ID="X_43", classes=["center", "incident"])
            X_192 = eval_trilinear_point(model, A, B, C, 'b*c*(c*a + a*b - b*c)', ID="X_192", classes=["center", "incident"])
            central_line(model, X_43, X_192, 43, 192, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_321 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(2)*c**(2)', ID="X_321", classes=["center", "incident"])
            central_line(model, X_10, X_321, 10, 321, incident=True)
            X_171 = eval_trilinear_point(model, A, B, C, 'a**(2) + b*c', ID="X_171", 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_171, X_190, 171, 190, incident=True)
            return promote_point_to_top(model, X_3971)


        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_3971 on the given reference triangle."""
            model = create_model('X_3971 = X_2com[INVERSE(n(INCENTRAL TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03971(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-03971.json"))
            write_center_svg(
                model_acute,
                here / "x-03971.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3971¶

X₃₉₇₁¶