← etc / Encyclopedia of Triangle Centers

X₂₇₃₃¶

SR(X₁₀₂, X₁₀₈)

X₂₇₃₃ = reflection of X₂₇₆₅ in X₃

X₂₇₃₃ (SR(X₁₀₂, X₁₀₈)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2733 = SR(X_102, 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_02733(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2733 = SR(X_102, X_108) on reference triangle ABC."""
            X_102 = eval_trilinear_point(model, A, B, C, '1/(sin(B)*(sec(A) - sec(B)) + sin(C)*(sec(A) - sec(C)))', ID="X_102", classes=["center"])
            X_521 = eval_trilinear_point(model, A, B, C, '(sec(B) - sec(C))*(csc(A))', ID="X_521", classes=["center"])
            X_108 = eval_trilinear_point(model, A, B, C, 'a/(sec(B) - sec(C))', ID="X_108", classes=["center"])
            X_515 = eval_trilinear_point(model, A, B, C, '(b + c)*sec(A) - b*sec(B) - c*sec(C)', ID="X_515", classes=["center"])
            central_line(model, X_102, X_521, 102, 521)
            central_line(model, X_108, X_515, 108, 515)
            X_2733 = intersect_lines(model, X_102, X_521, X_108, X_515, ID="X_2733", classes=["selected", "target"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            X_1295 = point_from_barycentrics(model, A, B, C, 0.79525862, 0.88362069, -0.67887931, ID="X_1295", classes=["center", "incident"])
            central_line(model, X_522, X_1295, 522, 1295, incident=True)
            return promote_point_to_top(model, X_2733)


        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_2733 on the given reference triangle."""
            model = create_model('X_2733 = SR(X_102, X_108)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02733(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-02733.json"))
            write_center_svg(
                model_acute,
                here / "x-02733.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2733¶

X₂₇₃₃¶