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X₃₂₆₃¶

ISOTOMIC CONJUGATE OF X₁₀₅

X₃₂₆₃ is the isotomic conjugate of X₁₀₅.

X₃₂₆₃ (ISOTOMIC CONJUGATE OF X₁₀₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3263 = ISOTOMIC CONJUGATE OF X_105."""

        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_03263(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3263 = ISOTOMIC CONJUGATE OF X_105 on reference triangle ABC."""
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center"])
            X_3263 = isotomic_conjugate(model, A, B, C, X_105, ID="X_3263", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_2, X_37, 2, 37, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_304 = eval_trilinear_point(model, A, B, C, '(cot(A))*(csc(A))**(2)', ID="X_304", classes=["center", "incident"])
            central_line(model, X_8, X_304, 8, 304, incident=True)
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center", "incident"])
            X_341 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)*(b + c - a)**(2)', ID="X_341", classes=["center", "incident"])
            central_line(model, X_85, X_341, 85, 341, incident=True)
            return promote_point_to_top(model, X_3263)


        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_3263 on the given reference triangle."""
            model = create_model('X_3263 = ISOTOMIC CONJUGATE OF X_105')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03263(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-03263.json"))
            write_center_svg(
                model_acute,
                here / "x-03263.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3263¶

X₃₂₆₃¶