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X₃₈₃₉¶

X₃₅₄₅com(EULER TRIANGLE)

X₃₈₃₉ = trisector nearest X₄ of segment X₂ X₄

X₃₈₃₉ (X₃₅₄₅com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3839 = X_3545com(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_03839(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3839 = X_3545com(EULER TRIANGLE) on reference triangle ABC."""
            X_3839 = eval_barycentric_point(model, A, B, C, '5*a**(4) - 7*b**(4) - 7*c**(4) + 2*a**(2)*b**(2) + 2*a**(2)*c**(2) + 14*b**(2)*c**(2)', ID="X_3839", 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_147 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(8) + (b**(2) + c**(2))*a**(6) - (2*b**(4) + 3*b**(2)*c**(2) + 2*c**(4))*a**(4) + (b**(6) + b**(4)*c**(2) + b**(2)*c**(4) + c**(6))*a**(2) - b**(8) + b**(6)*c**(2) + b**(2)*c**(6) - c**(8))', ID="X_147", classes=["center", "incident"])
            X_671 = eval_trilinear_point(model, A, B, C, '1/(a*(2*a**(2) - b**(2) - c**(2)))', ID="X_671", classes=["center", "incident"])
            central_line(model, X_147, X_671, 147, 671, incident=True)
            X_519 = eval_trilinear_point(model, A, B, C, '(2*a - b - c)/a', ID="X_519", classes=["center", "incident"])
            X_1699 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A) + cos(B) + cos(C) - 1', ID="X_1699", classes=["center", "incident"])
            central_line(model, X_519, X_1699, 519, 1699, incident=True)
            return promote_point_to_top(model, X_3839)


        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_3839 on the given reference triangle."""
            model = create_model('X_3839 = X_3545com(EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03839(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-03839.json"))
            write_center_svg(
                model_acute,
                here / "x-03839.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3839¶

X₃₈₃₉¶