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X₁₀₂₉¶

CYCLOCEVIAN CONJUGATE OF X₁

X₁₀₂₉ (CYCLOCEVIAN CONJUGATE OF X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1029 = CYCLOCEVIAN CONJUGATE OF X_1."""

        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,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01029(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1029 = CYCLOCEVIAN CONJUGATE OF X_1 on reference triangle ABC."""
            X_1029 = eval_trilinear_point(model, A, B, C, '(1/(a + 2*(a + b + c)*cos(A)))', ID="X_1029", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_191 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(b*c + c*a + a*b) + b**(3) + c**(3) - a**(3)', ID="X_191", classes=["center", "incident"])
            central_line(model, X_10, X_191, 10, 191, incident=True)
            X_319 = eval_trilinear_point(model, A, B, C, '(1 + 2*cos(A))/a**(2)', ID="X_319", classes=["center", "incident"])
            X_321 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(2)*c**(2)', ID="X_321", classes=["center", "incident"])
            central_line(model, X_319, X_321, 319, 321, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_593 = eval_trilinear_point(model, A, B, C, 'a/(b + c)**(2)', ID="X_593", classes=["center", "incident"])
            central_line(model, X_115, X_593, 115, 593, incident=True)
            return promote_point_to_top(model, X_1029)


        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_1029 on the given reference triangle."""
            model = create_model('X_1029 = CYCLOCEVIAN CONJUGATE OF X_1')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01029(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-01029.json"))
            write_center_svg(
                model_acute,
                here / "x-01029.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1029¶

X₁₀₂₉¶