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X₂₉₁₈¶

TANGENTIAL-ISOGONAL CONJUGATE OF X₅

X₂₉₁₈ is the tangential-isogonal conjugate of X₅.

X₂₉₁₈ (TANGENTIAL-ISOGONAL CONJUGATE OF X₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2918 = TANGENTIAL-ISOGONAL CONJUGATE OF X_5."""

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


        def construct_x_02918(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2918 = TANGENTIAL-ISOGONAL CONJUGATE OF X_5 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_26 = eval_trilinear_point(model, A, B, C, 'a*(b**(2)*cos(2*B) + c**(2)*cos(2*C) - a**(2)*cos(2*A))', ID="X_26", classes=["center"])
            X_22 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4))', ID="X_22", classes=["center"])
            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"])
            central_line(model, X_6, X_26, 6, 26)
            central_line(model, X_22, X_155, 22, 155)
            X_2918 = intersect_lines(model, X_6, X_26, X_22, X_155, ID="X_2918", classes=["selected", "target"])
            X_184 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A)', ID="X_184", classes=["center", "incident"])
            X_195 = eval_trilinear_point(model, A, B, C, 'a*(a**(8) + b**(8) + c**(8) - 4*a**(6)*(b**(2) + c**(2)) + a**(4)*(6*b**(4) + 6*c**(4) + 5*b**(2)*c**(2)) - a**(2)*(4*b**(6) + 4*c**(6) - b**(4)*c**(2) - b**(2)*c**(4)) - 2*b**(2)*c**(2)*(b**(4) + c**(4) - b**(2)*c**(2)))', ID="X_195", classes=["center", "incident"])
            central_line(model, X_184, X_195, 184, 195, incident=True)
            return promote_point_to_top(model, X_2918)


        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_2918 on the given reference triangle."""
            model = create_model('X_2918 = TANGENTIAL-ISOGONAL CONJUGATE OF X_5')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02918(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-02918.json"))
            write_center_svg(
                model_acute,
                here / "x-02918.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2918¶

X₂₉₁₈¶