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X₁₀₂₁¶

ISOGONAL CONJUGATE OF X₁₀₂₀

X₁₀₂₁ is the isogonal conjugate of X₁₀₂₀.

X₁₀₂₁ (ISOGONAL CONJUGATE OF X₁₀₂₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1021 = ISOGONAL CONJUGATE OF X_1020."""

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


        def construct_x_01021(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1021 = ISOGONAL CONJUGATE OF X_1020 on reference triangle ABC."""
            X_1020 = eval_trilinear_point(model, A, B, C, '(cos(B) + cos(C))/(cos(B) - cos(C))', ID="X_1020", classes=["center"])
            X_1021 = isogonal_conjugate(model, A, B, C, X_1020, ID="X_1021", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_647 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2))', ID="X_647", classes=["center", "incident"])
            central_line(model, X_1, X_647, 1, 647, incident=True)
            X_239 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) - b*c)', ID="X_239", classes=["center", "incident"])
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            central_line(model, X_239, X_514, 239, 514, incident=True)
            X_243 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(2) - cos(B)*cos(C))', ID="X_243", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_243, X_522, 243, 522, incident=True)
            return promote_point_to_top(model, X_1021)


        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_1021 on the given reference triangle."""
            model = create_model('X_1021 = ISOGONAL CONJUGATE OF X_1020')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01021(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-01021.json"))
            write_center_svg(
                model_acute,
                here / "x-01021.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1021¶

X₁₀₂₁¶