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X₁₁₄₆¶

CENTER OF HYPERBOLA {{A,B,C,X₂,X₈}}

X₁₁₄₆ = midpoint of X₂ and X₁₁₂₁

X₁₁₄₆ (CENTER OF HYPERBOLA {{A,B,C,X₂,X₈}}) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1146 = CENTER OF HYPERBOLA {{A,B,C,X_2,X_8}}."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            midpoint,
            mittenpunkt_of,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01146(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1146 = CENTER OF HYPERBOLA {{A,B,C,X_2,X_8}} on reference triangle ABC."""
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_1121 = eval_trilinear_point(model, A, B, C, '(b*c/((b + c - a)*a - (a + b - c)*(a + c - b)))', ID="X_1121", classes=["center"])
            X_1146 = midpoint(model, X_2, X_1121, ID="X_1146", classes=["selected", "target"], guide=False)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            central_line(model, X_9, X_80, 9, 80, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_220 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)**(2)', ID="X_220", classes=["center", "incident"])
            central_line(model, X_8, X_220, 8, 220, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_124 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - a)*(b - c)**(2)*((b + c)*(b**(2) + c**(2) - a**(2) - b*c) + a*b*c))', ID="X_124", classes=["center", "incident"])
            central_line(model, X_115, X_124, 115, 124, incident=True)
            return promote_point_to_top(model, X_1146)


        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_1146 on the given reference triangle."""
            model = create_model('X_1146 = CENTER OF HYPERBOLA {{A,B,C,X_2,X_8}}')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01146(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-01146.json"))
            write_center_svg(
                model_acute,
                here / "x-01146.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1146¶

X₁₁₄₆¶