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X₁₂₅₁¶

ISOGONAL CONJUGATE OF X₁₀₈₂

X₁₂₅₁ is the isogonal conjugate of X₁₀₈₂.

X₁₂₅₁ (ISOGONAL CONJUGATE OF X₁₀₈₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1251 = ISOGONAL CONJUGATE OF X_1082."""

        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,
            incenter_of,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01251(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1251 = ISOGONAL CONJUGATE OF X_1082 on reference triangle ABC."""
            X_1082 = eval_trilinear_point(model, A, B, C, '(sec(A/2))*sin(A/2 -  pi  /3)', ID="X_1082", classes=["center"])
            X_1251 = isogonal_conjugate(model, A, B, C, X_1082, ID="X_1251", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_15 = eval_trilinear_point(model, A, B, C, 'sin(A +  pi  /3)', ID="X_15", classes=["center", "incident"])
            central_line(model, X_1, X_15, 1, 15, incident=True)
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_13, X_80, 13, 80, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_199 = eval_trilinear_point(model, A, B, C, '(a*(b**(4) + c**(4) - a**(4) + (b**(2) + c**(2) - a**(2))*(b*c + c*a + a*b)))', ID="X_199", classes=["center", "incident"])
            central_line(model, X_55, X_199, 55, 199, incident=True)
            return promote_point_to_top(model, X_1251)


        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_1251 on the given reference triangle."""
            model = create_model('X_1251 = ISOGONAL CONJUGATE OF X_1082')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01251(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-01251.json"))
            write_center_svg(
                model_acute,
                here / "x-01251.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1251¶

X₁₂₅₁¶