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X₂₅₇₈¶

X₂-ISOCONJUGATE OF X₁₁₁₃

X₂₅₇₈ (X₂-ISOCONJUGATE OF X₁₁₁₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2578 = X_2-ISOCONJUGATE OF X_1113."""

        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,
            intersect_lines,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02578(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2578 = X_2-ISOCONJUGATE OF X_1113 on reference triangle ABC."""
            X_44 = eval_trilinear_point(model, A, B, C, 'b + c - 2*a', ID="X_44", classes=["center"])
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center"])
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center"])
            X_1822 = point_from_barycentrics(model, A, B, C, -0.19858607, 0.24538924, 0.95319683, ID="X_1822", classes=["center"])
            central_line(model, X_44, X_513, 44, 513)
            central_line(model, X_163, X_1822, 163, 1822)
            X_2578 = intersect_lines(model, X_44, X_513, X_163, X_1822, ID="X_2578", classes=["selected", "target"])
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            X_2574 = point_from_barycentrics(model, A, B, C, 0.74587942, -0.66059908, -0.085280338, ID="X_2574", classes=["center", "incident"])
            central_line(model, X_71, X_2574, 71, 2574, incident=True)
            return promote_point_to_top(model, X_2578)


        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_2578 on the given reference triangle."""
            model = create_model('X_2578 = X_2-ISOCONJUGATE OF X_1113')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02578(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-02578.json"))
            write_center_svg(
                model_acute,
                here / "x-02578.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2578¶

X₂₅₇₈¶