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X₃₈₄₅¶

X₃₈₁com(EULER TRIANGLE)

X₃₈₄₅ = orthocentroidal-circle-inverse of X₃₈₃₀

X₃₈₄₅ (X₃₈₁com(EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3845 = X_381com(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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03845(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3845 = X_381com(EULER TRIANGLE) on reference triangle ABC."""
            X_3845 = eval_barycentric_point(model, A, B, C, '4*a**(4) - 5*b**(4) - 5*c**(4) + a**(2)*b**(2) + a**(2)*c**(2) + 10*b**(2)*c**(2)', ID="X_3845", 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_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1327 = eval_trilinear_point(model, A, B, C, '(1/(sin(A) + 3*cos(A)))', ID="X_1327", classes=["center", "incident"])
            central_line(model, X_6, X_1327, 6, 1327, incident=True)
            X_343 = eval_trilinear_point(model, A, B, C, 'cot(A)*cos(B - C)', ID="X_343", classes=["center", "incident"])
            X_1531 = eval_trilinear_point(model, A, B, C, '(2*a**(4) - a**(2)*(b**(2) + c**(2)) - b**(4) - c**(4) + 2*b**(2)*c**(2))*(a**(5) - a*(b**(2) - c**(2))**(2) - 4*b*c*(b**(3)*cos(B) + c**(3)*cos(C)))', ID="X_1531", classes=["center", "incident"])
            central_line(model, X_343, X_1531, 343, 1531, incident=True)
            return promote_point_to_top(model, X_3845)


        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_3845 on the given reference triangle."""
            model = create_model('X_3845 = X_381com(EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03845(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-03845.json"))
            write_center_svg(
                model_acute,
                here / "x-03845.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3845¶

X₃₈₄₅¶