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X₃₀₆₅¶

ISOGONAL CONJUGATE OF X₄₈₄

X₃₀₆₅ is the isogonal conjugate of X₄₈₄.

X₃₀₆₅ (ISOGONAL CONJUGATE OF X₄₈₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3065 = ISOGONAL CONJUGATE OF X_484."""

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


        def construct_x_03065(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3065 = ISOGONAL CONJUGATE OF X_484 on reference triangle ABC."""
            X_484 = eval_trilinear_point(model, A, B, C, '1 + 2*(cos(A) - cos(B) - cos(C))', ID="X_484", classes=["center"])
            X_3065 = isogonal_conjugate(model, A, B, C, X_484, ID="X_3065", classes=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_79 = eval_trilinear_point(model, A, B, C, '1/(1 + 2*cos(A))', ID="X_79", classes=["center", "incident"])
            central_line(model, X_11, X_79, 11, 79, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_30, X_80, 30, 80, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_191 = eval_trilinear_point(model, A, B, C, '(b + c - a)*(b*c + c*a + a*b) + b**(3) + c**(3) - a**(3)', ID="X_191", classes=["center", "incident"])
            central_line(model, X_8, X_191, 8, 191, incident=True)
            return promote_point_to_top(model, X_3065)


        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_3065 on the given reference triangle."""
            model = create_model('X_3065 = ISOGONAL CONJUGATE OF X_484')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03065(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-03065.json"))
            write_center_svg(
                model_acute,
                here / "x-03065.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3065¶

X₃₀₆₅¶