← etc / Encyclopedia of Triangle Centers

X₁₂₄₁¶

ISOTOMIC CONJUGATE OF X₁₁₉₄

X₁₂₄₁ is the isotomic conjugate of X₁₁₉₄.

X₁₂₄₁ (ISOTOMIC CONJUGATE OF X₁₁₉₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1241 = ISOTOMIC CONJUGATE OF X_1194."""

        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,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01241(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1241 = ISOTOMIC CONJUGATE OF X_1194 on reference triangle ABC."""
            X_1194 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) + a**(2)*b**(2) + a**(2)*c**(2)))', ID="X_1194", classes=["center"])
            X_1241 = isotomic_conjugate(model, A, B, C, X_1194, ID="X_1241", classes=["selected", "target"])
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            central_line(model, X_25, X_76, 25, 76, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_305 = eval_trilinear_point(model, A, B, C, 'b**(4)*c**(4)*cos(A)', ID="X_305", classes=["center", "incident"])
            central_line(model, X_6, X_305, 6, 305, incident=True)
            X_251 = eval_trilinear_point(model, A, B, C, 'a**(2)*csc(A +  omega  )', ID="X_251", classes=["center", "incident"])
            X_384 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(4) + b**(2)*c**(2))', ID="X_384", classes=["center", "incident"])
            central_line(model, X_251, X_384, 251, 384, incident=True)
            return promote_point_to_top(model, X_1241)


        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_1241 on the given reference triangle."""
            model = create_model('X_1241 = ISOTOMIC CONJUGATE OF X_1194')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01241(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-01241.json"))
            write_center_svg(
                model_acute,
                here / "x-01241.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1241¶

X₁₂₄₁¶