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X₃₈₅₅¶

X₃₅₂₅com(EULER TRIANGLE)

X₃₈₅₅ = orthocentroidal circle inverse of X₃₅₂₉

X₃₈₅₅ (X₃₅₂₅com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3855 = X_3525com(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 (
            central_line,
            centroid_of,
            circumcenter_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_03855(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3855 = X_3525com(EULER TRIANGLE) on reference triangle ABC."""
            X_3855 = eval_barycentric_point(model, A, B, C, '(3*a**(4) - 7*b**(4) - 7*c**(4) + 4*a**(2)*b**(2) + 4*a**(2)*c**(2) + 14*b**(2)*c**(2))', ID="X_3855", 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_946 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(3)*(b + c) + (b - c)**(2)*(a**(2) - a*b - a*c - b**(2) - c**(2) - 2*b*c))', ID="X_946", classes=["center", "incident"])
            X_3632 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - 2*b - 2*c)', ID="X_3632", classes=["center", "incident"])
            central_line(model, X_946, X_3632, 946, 3632, incident=True)
            X_944 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a**(4) - 2*a**(3)*(b + c) + (b - c)**(2)*(2*a*b + 2*a*c - 2*b*c - b**(2) - c**(2) - 2*a**(2)))', ID="X_944", classes=["center", "incident"])
            X_3636 = eval_trilinear_point(model, A, B, C, 'b*c*(6*a + b + c)', ID="X_3636", classes=["center", "incident"])
            central_line(model, X_944, X_3636, 944, 3636, incident=True)
            return promote_point_to_top(model, X_3855)


        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_3855 on the given reference triangle."""
            model = create_model('X_3855 = X_3525com(EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03855(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-03855.json"))
            write_center_svg(
                model_acute,
                here / "x-03855.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3855¶

X₃₈₅₅¶