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X₂₅₄¶

X₃-CROSS CONJUGATE OF X₄

X₂₅₄ (X₃-CROSS CONJUGATE OF X₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_254 = X_3-CROSS CONJUGATE OF X_4."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            isogonal_conjugate,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00254(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_254 = X_3-CROSS CONJUGATE OF X_4 on reference triangle ABC."""
            X_155 = eval_trilinear_point(model, A, B, C, '(cos(A))*((cos(B))**(2) + (cos(C))**(2) - (cos(A))**(2))', ID="X_155", classes=["center"])
            X_254 = isogonal_conjugate(model, A, B, C, X_155, ID="X_254", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            central_line(model, X_4, X_155, 4, 155, incident=True)
            X_68 = eval_trilinear_point(model, A, B, C, 'cos(A)*sec(2*A)', ID="X_68", classes=["center", "incident"])
            X_136 = eval_barycentric_point(model, A, B, C, '(b**(2) - c**(2))**(2)*(a**(4) + b**(4) + c**(4) - 2*a**(2)*b**(2) - 2*a**(2)*c**(2))/(a**(2) - b**(2) - c**(2))', ID="X_136", classes=["center", "incident"])
            central_line(model, X_68, X_136, 68, 136, incident=True)
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            X_225 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(B) + cos(C))', ID="X_225", classes=["center", "incident"])
            central_line(model, X_46, X_225, 46, 225, incident=True)
            return promote_point_to_top(model, X_254)


        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_254 on the given reference triangle."""
            model = create_model('X_254 = X_3-CROSS CONJUGATE OF X_4')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00254(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-00254.json"))
            write_center_svg(
                model_acute,
                here / "x-00254.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X254¶

X₂₅₄¶