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X₄₀₅¶

EULER LINE INTERCEPT OF LINE X₁X_6

X₄₀₅ is the {X₂,X₃}-harmonic conjugate of X₄₇₄. For a list of harmonic conjugates of X₄₀₅, click Tables at the top of this page.

X₄₀₅ (EULER LINE INTERCEPT OF LINE X₁X_6) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_405 = EULER LINE INTERCEPT OF LINE X_1X_6."""

        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,
            circumcenter_of,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
            spieker_center_of,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00405(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_405 = EULER LINE INTERCEPT OF LINE X_1X_6 on reference triangle ABC."""
            X_377 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(4) + c**(4) - a**(4) - 2*b**(2)*c**(2) - 2*a*b*c*(a + b + c)))', ID="X_377", classes=["center"])
            X_405 = complement(model, A, B, C, X_377, ID="X_405", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_1, X_6, 1, 6, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            central_line(model, X_10, X_55, 10, 55, incident=True)
            return promote_point_to_top(model, X_405)


        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_405 on the given reference triangle."""
            model = create_model('X_405 = EULER LINE INTERCEPT OF LINE X_1X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00405(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-00405.json"))
            write_center_svg(
                model_acute,
                here / "x-00405.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X405¶

X₄₀₅¶