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X₂₁₀₅¶

REFLECTION OF X₁₁₁₄ IN X₆

X₂₁₀₅ is the reflection of X₁₁₁₄ in X₆.

X₂₁₀₅ (REFLECTION OF X₁₁₁₄ IN X₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2105 = REFLECTION OF X_1114 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,
            intersect_lines,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02105(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2105 = REFLECTION OF X_1114 IN X_6 on reference triangle ABC."""
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_1114 = eval_trilinear_point(model, A, B, C, '(R + d)*cos(A) - 2*R*cos(B)*cos(C)', ID="X_1114", classes=["center"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center"])
            X_1351 = eval_trilinear_point(model, A, B, C, 'a - R*cot(omega)*cos(A)', ID="X_1351", classes=["center"])
            central_line(model, X_6, X_1114, 6, 1114)
            central_line(model, X_30, X_1351, 30, 1351)
            X_2105 = intersect_lines(model, X_6, X_1114, X_30, X_1351, ID="X_2105", classes=["selected", "target"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_1312 = eval_trilinear_point(model, A, B, C, '((J - 1)*cos(A) + 2*(J + 1)*cos(B)*cos(C))', ID="X_1312", classes=["center", "incident"])
            central_line(model, X_69, X_1312, 69, 1312, incident=True)
            return promote_point_to_top(model, X_2105)


        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_2105 on the given reference triangle."""
            model = create_model('X_2105 = REFLECTION OF X_1114 IN X_6')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02105(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-02105.json"))
            write_center_svg(
                model_acute,
                here / "x-02105.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2105¶

X₂₁₀₅¶