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X₂₇₀₈¶

SR(X₉₈, X₁₀₉)

X₂₇₀₈ = reflection of X₂₇₀₁ in X₃

X₂₇₀₈ (SR(X₉₈, X₁₀₉)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2708 = SR(X_98, X_109)."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
            reflection_in_point,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02708(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2708 = SR(X_98, X_109) on reference triangle ABC."""
            X_2701 = eval_trilinear_point(model, A, B, C, '(a/((b - c)*(a**(3) + b**(3) + c**(3) - 2*a**(2)*b - 2*a**(2)*c + a*b*c)))', ID="X_2701", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_2708 = reflection_in_point(model, X_2701, X_3, ID="X_2708", classes=["selected", "target"], guide=False)
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center", "incident"])
            X_240 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(A +  omega  )', ID="X_240", classes=["center", "incident"])
            central_line(model, X_108, X_240, 108, 240, incident=True)
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            X_415 = eval_barycentric_point(model, A, B, C, '(a + b) * (a + c) * (a**(2) + b**(2) - c**(2)) * (a**(2) - b**(2) + c**(2)) * (a**(3) - 2*a**(2)*b + b**(3) - 2*a**(2)*c + a*b*c + c**(3))', ID="X_415", classes=["center", "incident"])
            central_line(model, X_107, X_415, 107, 415, incident=True)
            X_99 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(2) - c**(2))', ID="X_99", classes=["center", "incident"])
            X_515 = eval_trilinear_point(model, A, B, C, '(b + c)*sec(A) - b*sec(B) - c*sec(C)', ID="X_515", classes=["center", "incident"])
            central_line(model, X_99, X_515, 99, 515, incident=True)
            return promote_point_to_top(model, X_2708)


        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_2708 on the given reference triangle."""
            model = create_model('X_2708 = SR(X_98, X_109)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02708(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-02708.json"))
            write_center_svg(
                model_acute,
                here / "x-02708.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2708¶

X₂₇₀₈¶