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X₁₄₁₄¶

X₉₉-BETH CONJUGATE OF X₉₉

X₁₄₁₄ (X₉₉-BETH CONJUGATE OF X₉₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1414 = X_99-BETH CONJUGATE OF X_99."""

        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,
            gergonne_point_of,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01414(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1414 = X_99-BETH CONJUGATE OF X_99 on reference triangle ABC."""
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center"])
            X_85 = eval_trilinear_point(model, A, B, C, 'b**(2)*c**(2)/(b + c - a)', ID="X_85", classes=["center"])
            X_603 = eval_trilinear_point(model, A, B, C, '(cos(A))**(2) - cos(A)', ID="X_603", classes=["center"])
            central_line(model, X_99, X_109, 99, 109)
            central_line(model, X_85, X_603, 85, 603)
            X_1414 = intersect_lines(model, X_99, X_109, X_85, X_603, ID="X_1414", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_757 = eval_trilinear_point(model, A, B, C, '(b + c) **(-2)', ID="X_757", classes=["center", "incident"])
            central_line(model, X_7, X_757, 7, 757, incident=True)
            return promote_point_to_top(model, X_1414)


        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_1414 on the given reference triangle."""
            model = create_model('X_1414 = X_99-BETH CONJUGATE OF X_99')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01414(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-01414.json"))
            write_center_svg(
                model_acute,
                here / "x-01414.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1414¶

X₁₄₁₄¶