← etc / Encyclopedia of Triangle Centers

X₁₃₀₉¶

COLLINGS TRANSFORM OF X₈₆₀

X₁₃₀₉ (COLLINGS TRANSFORM OF X₈₆₀) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1309 = COLLINGS TRANSFORM OF X_860."""

        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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01309(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1309 = COLLINGS TRANSFORM OF X_860 on reference triangle ABC."""
            X_1309 = eval_trilinear_point(model, A, B, C, '(csc(2*A))/(4*((sin(B))**(2) - (sin(C))**(2))*cos(B)*cos(C) + (sin(B))**(2)*cos(B) - (sin(C))**(2)*cos(C))', ID="X_1309", classes=["selected", "target"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            X_243 = eval_trilinear_point(model, A, B, C, '(sec(A))*((cos(A))**(2) - cos(B)*cos(C))', ID="X_243", classes=["center", "incident"])
            central_line(model, X_105, X_243, 105, 243, incident=True)
            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", "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_102, X_515, 102, 515, incident=True)
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_109, X_522, 109, 522, incident=True)
            return promote_point_to_top(model, X_1309)


        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_1309 on the given reference triangle."""
            model = create_model('X_1309 = COLLINGS TRANSFORM OF X_860')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01309(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-01309.json"))
            write_center_svg(
                model_acute,
                here / "x-01309.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1309¶

X₁₃₀₉¶