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X₃₁₈₀¶

X₁₃-CEVA CONJUGATE OF X₂

X₃₁₈₀ (X₁₃-CEVA CONJUGATE OF X₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3180 = X_13-CEVA CONJUGATE OF X_2."""

        from __future__ import annotations

        from pathlib import Path

        import sympy.geometry as spg
        from geometor.model import Model

        from geometor.etc.ops import (
            anticomplement,
            central_line,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03180(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3180 = X_13-CEVA CONJUGATE OF X_2 on reference triangle ABC."""
            X_298 = eval_trilinear_point(model, A, B, C, '(csc(A))**(2)*sin(A +  pi  /3)', ID="X_298", classes=["center"])
            X_3180 = anticomplement(model, A, B, C, X_298, ID="X_3180", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            X_533 = point_from_barycentrics(model, A, B, C, 0.76482932, -0.13487259, -0.62995674, ID="X_533", classes=["center", "incident"])
            central_line(model, X_13, X_533, 13, 533, incident=True)
            X_148 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) - (b**(2) - c**(2))**(2) + b**(2)*c**(2) - a**(2)*b**(2) - a**(2)*c**(2))', ID="X_148", classes=["center", "incident"])
            X_531 = point_from_barycentrics(model, A, B, C, -0.19452926, 0.78400969, -0.58948043, ID="X_531", classes=["center", "incident"])
            central_line(model, X_148, X_531, 148, 531, incident=True)
            return promote_point_to_top(model, X_3180)


        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_3180 on the given reference triangle."""
            model = create_model('X_3180 = X_13-CEVA CONJUGATE OF X_2')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03180(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-03180.json"))
            write_center_svg(
                model_acute,
                here / "x-03180.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3180¶

X₃₁₈₀¶