← etc / Encyclopedia of Triangle Centers

X₁₃₁₁¶

COLLINGS TRANSFORM OF X₁₁₄₆

X₁₃₁₁ (COLLINGS TRANSFORM OF X₁₁₄₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1311 = COLLINGS TRANSFORM OF X_1146."""

        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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01311(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1311 = COLLINGS TRANSFORM OF X_1146 on reference triangle ABC."""
            X_1311 = eval_barycentric_point(model, A, B, C, '1/(a**(2)*(b**(2) + c**(2)) - a*b*c*(b + c) - (b - c)**(2)*(b**(2) + b*c + c**(2)))', ID="X_1311", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center", "incident"])
            central_line(model, X_8, X_101, 8, 101, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            central_line(model, X_2, X_109, 2, 109, incident=True)
            X_29 = eval_trilinear_point(model, A, B, C, '(sec(A))/(cos(B) + cos(C))', ID="X_29", classes=["center", "incident"])
            X_112 = eval_trilinear_point(model, A, B, C, 'a/(sin(2*B) - sin(2*C))', ID="X_112", classes=["center", "incident"])
            central_line(model, X_29, X_112, 29, 112, incident=True)
            return promote_point_to_top(model, X_1311)


        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_1311 on the given reference triangle."""
            model = create_model('X_1311 = COLLINGS TRANSFORM OF X_1146')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01311(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-01311.json"))
            write_center_svg(
                model_acute,
                here / "x-01311.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1311¶

X₁₃₁₁¶