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X₂₀₉₉¶

REFLECTION OF X₅₅ IN X₁

X₂₀₉₉ is the reflection of X₅₅ in X₁.

X₂₀₉₉ (REFLECTION OF X₅₅ IN X₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2099 = REFLECTION OF X_55 IN X_1."""

        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,
            nagel_point_of,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02099(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2099 = REFLECTION OF X_55 IN X_1 on reference triangle ABC."""
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_2099 = reflection_in_point(model, X_55, X_1, ID="X_2099", classes=["selected", "target"], guide=False)
            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_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_8, X_12, 8, 12, incident=True)
            X_80 = eval_trilinear_point(model, A, B, C, '1/(1 - 2*cos(A))', ID="X_80", classes=["center", "incident"])
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center", "incident"])
            central_line(model, X_80, X_381, 80, 381, incident=True)
            return promote_point_to_top(model, X_2099)


        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_2099 on the given reference triangle."""
            model = create_model('X_2099 = REFLECTION OF X_55 IN X_1')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02099(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-02099.json"))
            write_center_svg(
                model_acute,
                here / "x-02099.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2099¶

X₂₀₉₉¶