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X₃₆₃₉¶

OUTER SODDY-GERGONNE POINT

X₃₆₃₉ = X₁₆-of-intouch-triangle

X₃₆₃₉ (OUTER SODDY-GERGONNE POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3639 = OUTER SODDY-GERGONNE POINT."""

        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_barycentric_point,
            eval_trilinear_point,
            gergonne_point_of,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03639(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3639 = OUTER SODDY-GERGONNE POINT on reference triangle ABC."""
            X_3639 = eval_barycentric_point(model, A, B, C, '(2*(2*a**(2)-(b+c)*a-(b-c)**(2))*S+sqrt(3)*(-a+b+c) * (2*a**(3)-(b+c)*a**(2)-(b**(2)-c**(2)) * (b-c))) * (a-b+c) * (a+b-c)', ID="X_3639", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_1, X_7, 1, 7, incident=True)
            X_13 = eval_trilinear_point(model, A, B, C, 'csc(A +  pi  /3)', ID="X_13", classes=["center", "incident"])
            X_226 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cos(B) + cos(C))', ID="X_226", classes=["center", "incident"])
            central_line(model, X_13, X_226, 13, 226, incident=True)
            X_553 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a + b + c)/(b + c - a)', ID="X_553", classes=["center", "incident"])
            X_559 = eval_trilinear_point(model, A, B, C, '(sec(A/2))*sin(A/2 +  pi  /3)', ID="X_559", classes=["center", "incident"])
            central_line(model, X_553, X_559, 553, 559, incident=True)
            return promote_point_to_top(model, X_3639)


        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_3639 on the given reference triangle."""
            model = create_model('X_3639 = OUTER SODDY-GERGONNE POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03639(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-03639.json"))
            write_center_svg(
                model_acute,
                here / "x-03639.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3639¶

X₃₆₃₉¶