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X₁₀₇₄¶

POINT ALNITAK

X₁₀₇₄ (POINT ALNITAK) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1074 = POINT ALNITAK."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01074(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1074 = POINT ALNITAK on reference triangle ABC."""
            X_1074 = eval_trilinear_point(model, A, B, C, '(cos(A) + (cos(B))**(2)*cos(C) + cos(B)*(cos(C))**(2))', ID="X_1074", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_224 = eval_trilinear_point(model, A, B, C, '(cot(B)*(cos(B/2))**(2) + cot(C)*(cos(C/2))**(2) - cot(A)*(cos(A/2))**(2))*cot(A)', ID="X_224", classes=["center", "incident"])
            central_line(model, X_1, X_224, 1, 224, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_225 = eval_trilinear_point(model, A, B, C, '(sec(A))*(cos(B) + cos(C))', ID="X_225", classes=["center", "incident"])
            central_line(model, X_3, X_225, 3, 225, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_1040 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(A)*cos(B)*cos(C)', ID="X_1040", classes=["center", "incident"])
            central_line(model, X_4, X_1040, 4, 1040, incident=True)
            return promote_point_to_top(model, X_1074)


        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_1074 on the given reference triangle."""
            model = create_model('X_1074 = POINT ALNITAK')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01074(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-01074.json"))
            write_center_svg(
                model_acute,
                here / "x-01074.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1074¶

X₁₀₇₄¶