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X₃₄₅₀¶

1st SARAGOSSA POINT OF X₈

X₃₄₅₀ = complementary conjugate of X₃₄₅₂

X₃₄₅₀ (1st SARAGOSSA POINT OF X₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3450 = 1st SARAGOSSA POINT OF 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            nagel_point_of,
            point_from_barycentrics,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03450(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3450 = 1st SARAGOSSA POINT OF X_8 on reference triangle ABC."""
            X_1329 = eval_trilinear_point(model, A, B, C, '(b*c*(b**(2)/(a - b + c) + c**(2)/(a + b - c)))', ID="X_1329", classes=["center"])
            X_3450 = isogonal_conjugate(model, A, B, C, X_1329, ID="X_3450", classes=["selected", "target"])
            X_35 = eval_trilinear_point(model, A, B, C, '1 + 2*cos(A)', ID="X_35", classes=["center", "incident"])
            X_572 = eval_trilinear_point(model, A, B, C, '(cos(A - U))', ID="X_572", classes=["center", "incident"])
            central_line(model, X_35, X_572, 35, 572, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_1397 = eval_trilinear_point(model, A, B, C, '((sin(A)*sin(A/2))**(2))', ID="X_1397", classes=["center", "incident"])
            central_line(model, X_8, X_1397, 8, 1397, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_1603 = point_from_barycentrics(model, A, B, C, 1.1738452, 1.1872659, -1.3611111, ID="X_1603", classes=["center", "incident"])
            central_line(model, X_6, X_1603, 6, 1603, incident=True)
            return promote_point_to_top(model, X_3450)


        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_3450 on the given reference triangle."""
            model = create_model('X_3450 = 1st SARAGOSSA POINT OF X_8')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03450(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-03450.json"))
            write_center_svg(
                model_acute,
                here / "x-03450.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3450¶

X₃₄₅₀¶