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X₁₀₄₈¶

POINT ALGIEBA

X₁₀₄₈ (POINT ALGIEBA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1048 = POINT ALGIEBA."""

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


        def construct_x_01048(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1048 = POINT ALGIEBA on reference triangle ABC."""
            X_1048 = eval_trilinear_point(model, A, B, C, 'a**(7)*(b**(2) + b*c + c**(2)) + a**(6)*(b + c)*(b**(2) + b*c + c**(2)) - a**(5)*(2*b**(4) + b**(3)*c + b*c**(3) + 2*c**(4)) - 2*a**(4)*(b + c)**(3)*(b**(2) - b*c + c**(2)) + a**(3)*(b**(6) - b**(5)*c - 2*b**(4)*c**(2) - b**(3)*c**(3) - 2*b**(2)*c**(4) - b*c**(5) + c**(6)) + a**(2)*(b**(7) + 2*b**(6)*c - 2*b**(4)*c**(3) - 2*b**(3)*c**(4) + 2*b*c**(6) + c**(7)) + a*b*c*(b**(2) - c**(2))**(2)*(b**(2) + c**(2)) - b**(2)*c**(2)*(b - c)**(2)*(b + c)**(3)', ID="X_1048", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_564 = eval_trilinear_point(model, A, B, C, 'cos(2*B - 2*C)', ID="X_564", classes=["center", "incident"])
            central_line(model, X_1, X_564, 1, 564, incident=True)
            X_484 = eval_trilinear_point(model, A, B, C, '1 + 2*(cos(A) - cos(B) - cos(C))', ID="X_484", classes=["center", "incident"])
            X_1046 = point_from_barycentrics(model, A, B, C, 0.13236391, 0.3064877, 0.5611484, ID="X_1046", classes=["center", "incident"])
            central_line(model, X_484, X_1046, 484, 1046, incident=True)
            return promote_point_to_top(model, X_1048)


        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_1048 on the given reference triangle."""
            model = create_model('X_1048 = POINT ALGIEBA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01048(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-01048.json"))
            write_center_svg(
                model_acute,
                here / "x-01048.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1048¶

X₁₀₄₈¶