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X₁₀₅₇¶

ISOGONAL CONJUGATE OF X₁₀₅₆

X₁₀₅₇ is the isogonal conjugate of X₁₀₅₆.

X₁₀₅₇ (ISOGONAL CONJUGATE OF X₁₀₅₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1057 = ISOGONAL CONJUGATE OF X_1056."""

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


        def construct_x_01057(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1057 = ISOGONAL CONJUGATE OF X_1056 on reference triangle ABC."""
            X_1056 = eval_trilinear_point(model, A, B, C, '(2 + cos(B)*cos(C))', ID="X_1056", classes=["center"])
            X_1057 = isogonal_conjugate(model, A, B, C, X_1056, ID="X_1057", classes=["selected", "target"])
            X_78 = eval_trilinear_point(model, A, B, C, '1/(1 - sec(A))', ID="X_78", classes=["center", "incident"])
            X_392 = eval_trilinear_point(model, A, B, C, '(b + c)*(b**(2) + c**(2) - a**(2)) + 4*a*b*c', ID="X_392", classes=["center", "incident"])
            central_line(model, X_78, X_392, 78, 392, incident=True)
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            X_999 = eval_trilinear_point(model, A, B, C, '2 - cos(A)', ID="X_999", classes=["center", "incident"])
            central_line(model, X_77, X_999, 77, 999, incident=True)
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_1058 = eval_trilinear_point(model, A, B, C, '(2 - cos(B)*cos(C))', ID="X_1058", classes=["center", "incident"])
            central_line(model, X_29, X_1058, 29, 1058, incident=True)
            return promote_point_to_top(model, X_1057)


        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_1057 on the given reference triangle."""
            model = create_model('X_1057 = ISOGONAL CONJUGATE OF X_1056')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01057(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-01057.json"))
            write_center_svg(
                model_acute,
                here / "x-01057.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1057¶

X₁₀₅₇¶