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X₂₆₉₈¶

SR(X₉₈, X₉₉)

X₂₆₉₈ = reflection of X₉₈ in the Brocard axis

X₂₆₉₈ (SR(X₉₈, X₉₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2698 = SR(X_98, 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_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02698(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2698 = SR(X_98, X_99) on reference triangle ABC."""
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center"])
            X_237 = eval_trilinear_point(model, A, B, C, 'a**(2)*cos(A +  omega  )', ID="X_237", classes=["center"])
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center"])
            X_419 = eval_barycentric_point(model, A, B, C, '(a**(2) - b*c) * (a**(2) + b*c) * (a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2))', ID="X_419", classes=["center"])
            central_line(model, X_110, X_237, 110, 237)
            central_line(model, X_107, X_419, 107, 419)
            X_2698 = intersect_lines(model, X_110, X_237, X_107, X_419, ID="X_2698", classes=["selected", "target"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_512 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) - c**(2))', ID="X_512", classes=["center", "incident"])
            central_line(model, X_98, X_512, 98, 512, incident=True)
            return promote_point_to_top(model, X_2698)


        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_2698 on the given reference triangle."""
            model = create_model('X_2698 = SR(X_98, X_99)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02698(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-02698.json"))
            write_center_svg(
                model_acute,
                here / "x-02698.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2698¶

X₂₆₉₈¶