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X₁₂₆₉¶

ISOTOMIC CONJUGATE OF X₁₁₂₆

X₁₂₆₉ is the isotomic conjugate of X₁₁₂₆.

X₁₂₆₉ (ISOTOMIC CONJUGATE OF X₁₁₂₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1269 = ISOTOMIC CONJUGATE OF X_1126."""

        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,
            isotomic_conjugate,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01269(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1269 = ISOTOMIC CONJUGATE OF X_1126 on reference triangle ABC."""
            X_1126 = eval_trilinear_point(model, A, B, C, 'a/(2*a+b+c)', ID="X_1126", classes=["center"])
            X_1269 = isotomic_conjugate(model, A, B, C, X_1126, ID="X_1269", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_10, X_75, 10, 75, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_349 = eval_trilinear_point(model, A, B, C, '(cos(B) + cos(C))*(csc(A))**(3)', ID="X_349", classes=["center", "incident"])
            central_line(model, X_7, X_349, 7, 349, incident=True)
            X_79 = eval_trilinear_point(model, A, B, C, '1/(1 + 2*cos(A))', ID="X_79", classes=["center", "incident"])
            X_314 = eval_trilinear_point(model, A, B, C, '(b**(2)*c**(2)*(b + c - a)/(b + c))', ID="X_314", classes=["center", "incident"])
            central_line(model, X_79, X_314, 79, 314, incident=True)
            return promote_point_to_top(model, X_1269)


        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_1269 on the given reference triangle."""
            model = create_model('X_1269 = ISOTOMIC CONJUGATE OF X_1126')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01269(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-01269.json"))
            write_center_svg(
                model_acute,
                here / "x-01269.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1269¶

X₁₂₆₉¶