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X₂₄₅₂¶

REFLECTION OF X₁₃₁₆ IN X₆

X₂₄₅₂ is the reflection of X₁₃₁₆ in X₆.

X₂₄₅₂ (REFLECTION OF X₁₃₁₆ IN X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2452 = REFLECTION OF X_1316 IN X_6."""

        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_trilinear_point,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02452(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2452 = REFLECTION OF X_1316 IN X_6 on reference triangle ABC."""
            X_1316 = eval_trilinear_point(model, A, B, C, 'b*c*(sin(B - C))**(2) + a**(2)*sin(A - B)*sin(A - C)', ID="X_1316", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_2452 = reflection_in_point(model, X_1316, X_6, ID="X_2452", classes=["selected", "target"], guide=False)
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_6, X_523, 6, 523, incident=True)
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            X_648 = eval_trilinear_point(model, A, B, C, '1/(a*(b**(2) - c**(2))*(b**(2) + c**(2) - a**(2)))', ID="X_648", classes=["center", "incident"])
            central_line(model, X_98, X_648, 98, 648, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_1351 = eval_trilinear_point(model, A, B, C, 'a - R*cot(omega)*cos(A)', ID="X_1351", classes=["center", "incident"])
            central_line(model, X_30, X_1351, 30, 1351, incident=True)
            return promote_point_to_top(model, X_2452)


        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_2452 on the given reference triangle."""
            model = create_model('X_2452 = REFLECTION OF X_1316 IN X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02452(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-02452.json"))
            write_center_svg(
                model_acute,
                here / "x-02452.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2452¶

X₂₄₅₂¶