← etc / Encyclopedia of Triangle Centers

X₁₃₀₆¶

COLLINGS TRANSFORM OF X₆₃₉

X₁₃₀₆ (COLLINGS TRANSFORM OF X₆₃₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1306 = COLLINGS TRANSFORM OF X_639."""

        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_01306(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1306 = COLLINGS TRANSFORM OF X_639 on reference triangle ABC."""
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center"])
            X_493 = eval_trilinear_point(model, A, B, C, '1/(sin(A) + sin(B)*sin(C))', ID="X_493", classes=["center"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center"])
            X_637 = point_from_barycentrics(model, A, B, C, 0.40143148, 0.29769606, 0.30087247, ID="X_637", classes=["center"])
            central_line(model, X_111, X_493, 111, 493)
            central_line(model, X_98, X_637, 98, 637)
            X_1306 = intersect_lines(model, X_111, X_493, X_98, X_637, ID="X_1306", classes=["selected", "target"])
            return promote_point_to_top(model, X_1306)


        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_1306 on the given reference triangle."""
            model = create_model('X_1306 = COLLINGS TRANSFORM OF X_639')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01306(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-01306.json"))
            write_center_svg(
                model_acute,
                here / "x-01306.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1306¶

X₁₃₀₆¶