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X₁₂₃₂¶

ISOTOMIC CONJUGATE OF X₁₁₇₃

X₁₂₃₂ is the isotomic conjugate of X₁₁₇₃.

X₁₂₃₂ (ISOTOMIC CONJUGATE OF X₁₁₇₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1232 = ISOTOMIC CONJUGATE OF X_1173."""

        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,
            isotomic_conjugate,
            orthocenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01232(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1232 = ISOTOMIC CONJUGATE OF X_1173 on reference triangle ABC."""
            X_1173 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(4) - 3*a**(2)*(b**(2) + c**(2)) + (b**(2) - c**(2))**(2))', ID="X_1173", classes=["center"])
            X_1232 = isotomic_conjugate(model, A, B, C, X_1173, ID="X_1232", classes=["selected", "target"])
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_4, X_69, 4, 69, incident=True)
            X_95 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*sec(B - C)', ID="X_95", classes=["center", "incident"])
            X_252 = eval_trilinear_point(model, A, B, C, '(sec(B - C)/(1 - 2*cos(2*A)))', ID="X_252", classes=["center", "incident"])
            central_line(model, X_95, X_252, 95, 252, incident=True)
            X_313 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(3)*c**(3)', ID="X_313", classes=["center", "incident"])
            X_1227 = point_from_barycentrics(model, A, B, C, 0.58333333, 1.8875832e-16, 0.41666667, ID="X_1227", classes=["center", "incident"])
            central_line(model, X_313, X_1227, 313, 1227, incident=True)
            return promote_point_to_top(model, X_1232)


        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_1232 on the given reference triangle."""
            model = create_model('X_1232 = ISOTOMIC CONJUGATE OF X_1173')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01232(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-01232.json"))
            write_center_svg(
                model_acute,
                here / "x-01232.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1232¶

X₁₂₃₂¶