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X₂₃₁¶

X₂-CEVA CONJUGATE OF X₁₂₈

X₂₃₁ = radical center of cirumcircle, nine-point circle and Hutson-Parry circle

X₂₃₁ (X₂-CEVA CONJUGATE OF X₁₂₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_231 = X_2-CEVA CONJUGATE OF X_128."""

        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_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00231(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_231 = X_2-CEVA CONJUGATE OF X_128 on reference triangle ABC."""
            X_231 = eval_trilinear_point(model, A, B, C, '(cos(B))*(4*(sin(C))**(2) - 1)*(cos(A)*sin(B) - sin(A)*cos(B)) - (cos(C))*(4*(sin(B))**(2) - 1)*(cos(C)*sin(A) - sin(C)*cos(A))', ID="X_231", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_17 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /6)', ID="X_17", classes=["center", "incident"])
            central_line(model, X_6, X_17, 6, 17, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_96 = eval_trilinear_point(model, A, B, C, 'sec(2*A)*sec(B - C)', ID="X_96", classes=["center", "incident"])
            central_line(model, X_4, X_96, 4, 96, incident=True)
            X_50 = eval_trilinear_point(model, A, B, C, 'sin(3*A)', ID="X_50", classes=["center", "incident"])
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            central_line(model, X_50, X_115, 50, 115, incident=True)
            return promote_point_to_top(model, X_231)


        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_231 on the given reference triangle."""
            model = create_model('X_231 = X_2-CEVA CONJUGATE OF X_128')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00231(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-00231.json"))
            write_center_svg(
                model_acute,
                here / "x-00231.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X231¶

X₂₃₁¶