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X₁₃₈₉¶

ISOGONAL CONJUGATE OF X₁₃₈₅

X₁₃₈₉ is the isogonal conjugate of X₁₃₈₅.

X₁₃₈₉ (ISOGONAL CONJUGATE OF X₁₃₈₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1389 = ISOGONAL CONJUGATE OF X_1385."""

        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,
            nagel_point_of,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01389(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1389 = ISOGONAL CONJUGATE OF X_1385 on reference triangle ABC."""
            X_1385 = eval_trilinear_point(model, A, B, C, '16*( area )**(2) + a*(a + b + c)*(b**(2) + c**(2) - a**(2))', ID="X_1385", classes=["center"])
            X_1389 = isogonal_conjugate(model, A, B, C, X_1385, ID="X_1389", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_5, X_8, 5, 8, incident=True)
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_104 = eval_trilinear_point(model, A, B, C, '1/(-1 + cos(B) + cos(C))', ID="X_104", classes=["center", "incident"])
            central_line(model, X_65, X_104, 65, 104, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center", "incident"])
            central_line(model, X_21, X_517, 21, 517, incident=True)
            return promote_point_to_top(model, X_1389)


        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_1389 on the given reference triangle."""
            model = create_model('X_1389 = ISOGONAL CONJUGATE OF X_1385')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01389(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-01389.json"))
            write_center_svg(
                model_acute,
                here / "x-01389.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1389¶

X₁₃₈₉¶