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X₁₄₄₀¶

X₃₀₉-BETH CONJUGATE OF X₃₀₉

X₁₄₄₀ (X₃₀₉-BETH CONJUGATE OF X₃₀₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1440 = X_309-BETH CONJUGATE OF X_309."""

        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,
            cevapoint,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            gergonne_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01440(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1440 = X_309-BETH CONJUGATE OF X_309 on reference triangle ABC."""
            X_84 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C) - cos(A) - 1)', ID="X_84", classes=["center"])
            X_1422 = point_from_barycentrics(model, A, B, C, -0.022661722, -0.056036259, 1.078698, ID="X_1422", classes=["center"])
            X_1440 = cevapoint(model, A, B, C, X_84, X_1422, ID="X_1440", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center", "incident"])
            central_line(model, X_2, X_77, 2, 77, incident=True)
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_7, X_84, 7, 84, incident=True)
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            X_280 = eval_trilinear_point(model, A, B, C, '((csc(A/2))**(2))/(-1 - cos(A) + cos(B) + cos(C))', ID="X_280", classes=["center", "incident"])
            central_line(model, X_75, X_280, 75, 280, incident=True)
            return promote_point_to_top(model, X_1440)


        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_1440 on the given reference triangle."""
            model = create_model('X_1440 = X_309-BETH CONJUGATE OF X_309')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01440(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-01440.json"))
            write_center_svg(
                model_acute,
                here / "x-01440.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1440¶

X₁₄₄₀¶