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X₃₁₉₇¶

X₄₀-CEVA CONJUGATE OF X₅₅

X₃₁₉₇ = isogonal conjugate of the polar conjugate of X₃₁₇₆

X₃₁₉₇ (X₄₀-CEVA CONJUGATE OF X₅₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3197 = X_40-CEVA CONJUGATE OF X_55."""

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


        def construct_x_03197(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3197 = X_40-CEVA CONJUGATE OF X_55 on reference triangle ABC."""
            X_3197 = eval_barycentric_point(model, A, B, C, 'a**(2)*(a**(6) - 2*a**(5)*b - a**(4)*b**(2) + 4*a**(3)*b**(3) - a**(2)*b**(4) - 2*a*b**(5) + b**(6) - 2*a**(5)*c - 2*a**(4)*b*c + 2*a*b**(4)*c + 2*b**(5)*c - a**(4)*c**(2) + 2*a**(2)*b**(2)*c**(2) - b**(4)*c**(2) + 4*a**(3)*c**(3) - 4*b**(3)*c**(3) - a**(2)*c**(4) + 2*a*b*c**(4) - b**(2)*c**(4) - 2*a*c**(5) + 2*b*c**(5) + c**(6))', ID="X_3197", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            central_line(model, X_6, X_19, 6, 19, incident=True)
            X_48 = eval_trilinear_point(model, A, B, C, 'tan(B) + tan(C)', ID="X_48", classes=["center", "incident"])
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            central_line(model, X_48, X_55, 48, 55, incident=True)
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            central_line(model, X_64, X_71, 64, 71, incident=True)
            return promote_point_to_top(model, X_3197)


        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_3197 on the given reference triangle."""
            model = create_model('X_3197 = X_40-CEVA CONJUGATE OF X_55')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03197(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-03197.json"))
            write_center_svg(
                model_acute,
                here / "x-03197.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3197¶

X₃₁₉₇¶