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X₂₀₉₇¶

REFLECTION OF X₆ IN X₅₇

X₂₀₉₇ is the reflection of X₆ in X₅₇.

X₂₀₉₇ (REFLECTION OF X₆ IN X₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2097 = REFLECTION OF X_6 IN X_57."""

        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,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02097(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2097 = REFLECTION OF X_6 IN X_57 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_57 = eval_trilinear_point(model, A, B, C, '1/(b + c - a)', ID="X_57", classes=["center"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center"])
            X_329 = eval_trilinear_point(model, A, B, C, '( -1 - cos(A) + cos(B) + cos(C))*(csc(A))', ID="X_329", classes=["center"])
            central_line(model, X_6, X_57, 6, 57)
            central_line(model, X_141, X_329, 141, 329)
            X_2097 = intersect_lines(model, X_6, X_57, X_141, X_329, ID="X_2097", classes=["selected", "target"])
            X_527 = eval_barycentric_point(model, A, B, C, '2*a**(2) - a*(b + c) - (b - c)**(2)', ID="X_527", classes=["center", "incident"])
            X_599 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2) - 2*b**(2) - 2*c**(2))', ID="X_599", classes=["center", "incident"])
            central_line(model, X_527, X_599, 527, 599, incident=True)
            return promote_point_to_top(model, X_2097)


        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_2097 on the given reference triangle."""
            model = create_model('X_2097 = REFLECTION OF X_6 IN X_57')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02097(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-02097.json"))
            write_center_svg(
                model_acute,
                here / "x-02097.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2097¶

X₂₀₉₇¶