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X₁₁₇₅¶

1st SARAGOSSA POINT OF X₆₅

X₁₁₇₅ (1st SARAGOSSA POINT OF X₆₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1175 = 1st SARAGOSSA POINT OF X_65."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01175(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1175 = 1st SARAGOSSA POINT OF X_65 on reference triangle ABC."""
            X_442 = point_from_barycentrics(model, A, B, C, 0.3215734, 0.32603406, 0.35239254, ID="X_442", classes=["center"])
            X_1175 = isogonal_conjugate(model, A, B, C, X_442, ID="X_1175", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", classes=["center", "incident"])
            central_line(model, X_3, X_60, 3, 60, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_21, X_72, 21, 72, incident=True)
            X_28 = eval_trilinear_point(model, A, B, C, '(tan(A))/(b + c)', ID="X_28", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_28, X_65, 28, 65, incident=True)
            return promote_point_to_top(model, X_1175)


        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_1175 on the given reference triangle."""
            model = create_model('X_1175 = 1st SARAGOSSA POINT OF X_65')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01175(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-01175.json"))
            write_center_svg(
                model_acute,
                here / "x-01175.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1175¶

X₁₁₇₅¶