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X₁₂₅₄¶

ISOGONAL CONJUGATE OF X₁₀₉₈

X₁₂₅₄ is the isogonal conjugate of X₁₀₉₈.

X₁₂₅₄ (ISOGONAL CONJUGATE OF X₁₀₉₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1254 = ISOGONAL CONJUGATE OF X_1098."""

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


        def construct_x_01254(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1254 = ISOGONAL CONJUGATE OF X_1098 on reference triangle ABC."""
            X_1098 = eval_trilinear_point(model, A, B, C, '(1/(cos(B) + cos(C))**(2))', ID="X_1098", classes=["center"])
            X_1254 = isogonal_conjugate(model, A, B, C, X_1098, ID="X_1254", classes=["selected", "target"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_34 = eval_trilinear_point(model, A, B, C, '1 - sec(A)', ID="X_34", classes=["center", "incident"])
            central_line(model, X_31, X_34, 31, 34, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_42, X_65, 42, 65, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_201 = eval_trilinear_point(model, A, B, C, '(cos(A))*(1 + cos(B - C))', ID="X_201", classes=["center", "incident"])
            central_line(model, X_12, X_201, 12, 201, incident=True)
            return promote_point_to_top(model, X_1254)


        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_1254 on the given reference triangle."""
            model = create_model('X_1254 = ISOGONAL CONJUGATE OF X_1098')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01254(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-01254.json"))
            write_center_svg(
                model_acute,
                here / "x-01254.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1254¶

X₁₂₅₄¶