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X₁₂₃₁¶

ISOTOMIC CONJUGATE OF X₁₁₇₂

X₁₂₃₁ is the isotomic conjugate of X₁₁₇₂.

X₁₂₃₁ (ISOTOMIC CONJUGATE OF X₁₁₇₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1231 = ISOTOMIC CONJUGATE OF X_1172."""

        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,
            gergonne_point_of,
            intersect_lines,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01231(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1231 = ISOTOMIC CONJUGATE OF X_1172 on reference triangle ABC."""
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center"])
            X_331 = eval_trilinear_point(model, A, B, C, '(sec(A/2))**(2)*csc(2*A)', ID="X_331", classes=["center"])
            central_line(model, X_7, X_8, 7, 8)
            central_line(model, X_76, X_331, 76, 331)
            X_1231 = intersect_lines(model, X_7, X_8, X_76, X_331, ID="X_1231", classes=["selected", "target"])
            X_201 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(B - C))', ID="X_201", classes=["center", "incident"])
            X_307 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*(b + c)*(cos(A))/(b + c - a)', ID="X_307", classes=["center", "incident"])
            central_line(model, X_201, X_307, 201, 307, incident=True)
            return promote_point_to_top(model, X_1231)


        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_1231 on the given reference triangle."""
            model = create_model('X_1231 = ISOTOMIC CONJUGATE OF X_1172')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01231(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-01231.json"))
            write_center_svg(
                model_acute,
                here / "x-01231.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1231¶

X₁₂₃₁¶