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X₁₀₅₁¶

POINT ALGORAB

X₁₀₅₁ (POINT ALGORAB) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1051 = POINT ALGORAB."""

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


        def construct_x_01051(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1051 = POINT ALGORAB on reference triangle ABC."""
            X_1051 = eval_trilinear_point(model, A, B, C, '(3*a**(2) + b**(2) + c**(2) + b*c + 5*a*b + 5*a*c)', ID="X_1051", classes=["selected", "target"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            X_572 = eval_trilinear_point(model, A, B, C, '(cos(A - U))', ID="X_572", classes=["center", "incident"])
            central_line(model, X_165, X_572, 165, 572, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_748 = eval_trilinear_point(model, A, B, C, 'a**(2) - 2*b*c', ID="X_748", classes=["center", "incident"])
            central_line(model, X_1, X_748, 1, 748, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_846 = eval_trilinear_point(model, A, B, C, '(- a**(2) + b**(2) + c**(2) + b*c + c*a + a*b)', ID="X_846", classes=["center", "incident"])
            central_line(model, X_6, X_846, 6, 846, incident=True)
            return promote_point_to_top(model, X_1051)


        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_1051 on the given reference triangle."""
            model = create_model('X_1051 = POINT ALGORAB')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01051(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-01051.json"))
            write_center_svg(
                model_acute,
                here / "x-01051.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1051¶

X₁₀₅₁¶