← etc / Encyclopedia of Triangle Centers

X₂₆₉₄¶

SR(X₇₄, X₁₀₈)

X₂₆₉₄ = reflection of X₂₇₆₆ in X₃

X₂₆₉₄ (SR(X₇₄, X₁₀₈)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2694 = SR(X_74, X_108)."""

        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,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_02694(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2694 = SR(X_74, X_108) on reference triangle ABC."""
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center"])
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center"])
            X_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center"])
            central_line(model, X_30, X_108, 30, 108)
            central_line(model, X_74, X_521, 74, 521)
            X_2694 = intersect_lines(model, X_30, X_108, X_74, X_521, ID="X_2694", classes=["selected", "target"])
            X_20 = eval_trilinear_point(model, A, B, C, 'cos(A) - cos(B)*cos(C)', ID="X_20", classes=["center", "incident"])
            X_1290 = point_from_barycentrics(model, A, B, C, -0.096774194, 0.87096774, 0.22580645, ID="X_1290", classes=["center", "incident"])
            central_line(model, X_20, X_1290, 20, 1290, incident=True)
            return promote_point_to_top(model, X_2694)


        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_2694 on the given reference triangle."""
            model = create_model('X_2694 = SR(X_74, X_108)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02694(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-02694.json"))
            write_center_svg(
                model_acute,
                here / "x-02694.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2694¶

X₂₆₉₄¶