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X₇₇₅¶

ISOGONAL CONJUGATE OF X₇₇₄

X₇₇₅ (ISOGONAL CONJUGATE OF X₇₇₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_775 = ISOGONAL CONJUGATE OF X_774."""

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


        def construct_x_00775(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_775 = ISOGONAL CONJUGATE OF X_774 on reference triangle ABC."""
            X_774 = eval_trilinear_point(model, A, B, C, '(cos(B))**(2) + (cos(C))**(2)', ID="X_774", classes=["center"])
            X_775 = isogonal_conjugate(model, A, B, C, X_774, ID="X_775", classes=["selected", "target"])
            X_158 = eval_trilinear_point(model, A, B, C, '(sec(A))**(2)', ID="X_158", classes=["center", "incident"])
            X_255 = eval_trilinear_point(model, A, B, C, '(cos(A))**(2)', ID="X_255", classes=["center", "incident"])
            central_line(model, X_158, X_255, 158, 255, incident=True)
            X_225 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(B) + cos(C))', ID="X_225", classes=["center", "incident"])
            X_412 = eval_barycentric_point(model, A, B, C, '(a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(6) + a**(5)*b - 2*a**(4)*b**(2) - 2*a**(3)*b**(3) + a**(2)*b**(4) + a*b**(5) + a**(5)*c - a**(4)*b*c - a*b**(4)*c + b**(5)*c - 2*a**(4)*c**(2) + 2*a**(2)*b**(2)*c**(2) - 2*a**(3)*c**(3) - 2*b**(3)*c**(3) + a**(2)*c**(4) - a*b*c**(4) + a*c**(5) + b*c**(5))', ID="X_412", classes=["center", "incident"])
            central_line(model, X_225, X_412, 225, 412, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_801 = eval_trilinear_point(model, A, B, C, '((csc(A))/((cos(B))**(2) + (cos(C))**(2)))', ID="X_801", classes=["center", "incident"])
            central_line(model, X_10, X_801, 10, 801, incident=True)
            return promote_point_to_top(model, X_775)


        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_775 on the given reference triangle."""
            model = create_model('X_775 = ISOGONAL CONJUGATE OF X_774')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00775(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-00775.json"))
            write_center_svg(
                model_acute,
                here / "x-00775.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X775¶

X₇₇₅¶