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X₃₈₇₅¶

X₁₄₁com[INVERSE(n(3rd EULER TRIANGLE))]

X₃₈₇₅ (X₁₄₁com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3875 = X_141com[INVERSE(n(3rd EULER TRIANGLE))]."""

        from __future__ import annotations

        from pathlib import Path

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

        from geometor.etc.ops import (
            anticomplement,
            central_line,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            incenter_of,
            mittenpunkt_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03875(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3875 = X_141com[INVERSE(n(3rd EULER TRIANGLE))] on reference triangle ABC."""
            X_2321 = point_from_barycentrics(model, A, B, C, 0.47272727, 0.32727273, 0.2, ID="X_2321", classes=["center"])
            X_3875 = anticomplement(model, A, B, C, X_2321, ID="X_3875", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_1, X_75, 1, 75, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", 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_7, X_145, 7, 145, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", 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_9, X_192, 9, 192, incident=True)
            return promote_point_to_top(model, X_3875)


        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_3875 on the given reference triangle."""
            model = create_model('X_3875 = X_141com[INVERSE(n(3rd EULER TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03875(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-03875.json"))
            write_center_svg(
                model_acute,
                here / "x-03875.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3875¶

X₃₈₇₅¶