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X₂₀₉₃¶

REFLECTION OF X₁ IN X₅₇

X₂₀₉₃ is the reflection of X₁ in X₅₇.

X₂₀₉₃ (REFLECTION OF X₁ IN X₅₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2093 = REFLECTION OF X_1 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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02093(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2093 = REFLECTION OF X_1 IN X_57 on reference triangle ABC."""
            X_2093 = eval_trilinear_point(model, A, B, C, 'a**(3) + 3*(b + c)*a**(2) - (b + c)**(2)*a - 3*(b + c)*(b - c)**(2)', ID="X_2093", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            central_line(model, X_1, X_3, 1, 3, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_329 = eval_trilinear_point(model, A, B, C, '( -1 - cos(A) + cos(B) + cos(C))*(csc(A))', ID="X_329", classes=["center", "incident"])
            central_line(model, X_10, X_329, 10, 329, incident=True)
            X_200 = eval_trilinear_point(model, A, B, C, '(cot(A/2))**(2)', ID="X_200", classes=["center", "incident"])
            X_758 = eval_trilinear_point(model, A, B, C, 'a**(0)*(b**(3) + c**(3)) - a**(2)*(b**(1) + c**(1))', ID="X_758", classes=["center", "incident"])
            central_line(model, X_200, X_758, 200, 758, incident=True)
            return promote_point_to_top(model, X_2093)


        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_2093 on the given reference triangle."""
            model = create_model('X_2093 = REFLECTION OF X_1 IN X_57')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02093(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-02093.json"))
            write_center_svg(
                model_acute,
                here / "x-02093.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2093¶

X₂₀₉₃¶