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X₁₂₇₄¶

ISOTOMIC CONJUGATE OF X₁₁₄₃

X₁₂₇₄ is the isotomic conjugate of X₁₁₄₃.

X₁₂₇₄ (ISOTOMIC CONJUGATE OF X₁₁₄₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1274 = ISOTOMIC CONJUGATE OF X_1143."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isotomic_conjugate,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01274(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1274 = ISOTOMIC CONJUGATE OF X_1143 on reference triangle ABC."""
            X_1143 = eval_trilinear_point(model, A, B, C, 'csc(A)*tan(A/4)', ID="X_1143", classes=["center"])
            X_1274 = isotomic_conjugate(model, A, B, C, X_1143, ID="X_1274", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_177 = eval_trilinear_point(model, A, B, C, '(cos(B/2) + cos(C/2))*sec(A/2)', ID="X_177", classes=["center", "incident"])
            central_line(model, X_8, X_177, 8, 177, incident=True)
            X_174 = eval_trilinear_point(model, A, B, C, 'sec(A/2)', ID="X_174", classes=["center", "incident"])
            X_176 = eval_trilinear_point(model, A, B, C, '1 + sec(A/2)*cos(B/2)*cos(C/2)', ID="X_176", classes=["center", "incident"])
            central_line(model, X_174, X_176, 174, 176, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_1489 = eval_trilinear_point(model, A, B, C, '((csc(A))*(1 - cos(A/2) - sin(A/2)))', ID="X_1489", classes=["center", "incident"])
            central_line(model, X_2, X_1489, 2, 1489, incident=True)
            return promote_point_to_top(model, X_1274)


        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_1274 on the given reference triangle."""
            model = create_model('X_1274 = ISOTOMIC CONJUGATE OF X_1143')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01274(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-01274.json"))
            write_center_svg(
                model_acute,
                here / "x-01274.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1274¶

X₁₂₇₄¶