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X₁₂₉₂¶

COLLINGS TRANSFORM OF X₅₅

X₁₂₉₂ (COLLINGS TRANSFORM OF X₅₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1292 = COLLINGS TRANSFORM OF X_55."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01292(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1292 = COLLINGS TRANSFORM OF X_55 on reference triangle ABC."""
            X_1292 = eval_trilinear_point(model, A, B, C, '1/((b - c)*(a**(2) + b**(2) + c**(2) - 2*a*b - 2*a*c))', ID="X_1292", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_105 = eval_trilinear_point(model, A, B, C, '1/(b**(2) + c**(2) - a*(b + c))', ID="X_105", classes=["center", "incident"])
            central_line(model, X_3, X_105, 3, 105, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_120 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a*b*c - (b + c)*(a**(2) + (b - c)**(2)))*(b**(2) + c**(2) - a*b -a*c)', ID="X_120", classes=["center", "incident"])
            central_line(model, X_4, X_120, 4, 120, incident=True)
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            X_103 = eval_trilinear_point(model, A, B, C, 'a/((a - b)*cot(C) + (a - c)*cot(B))', ID="X_103", classes=["center", "incident"])
            central_line(model, X_40, X_103, 40, 103, incident=True)
            return promote_point_to_top(model, X_1292)


        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_1292 on the given reference triangle."""
            model = create_model('X_1292 = COLLINGS TRANSFORM OF X_55')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01292(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-01292.json"))
            write_center_svg(
                model_acute,
                here / "x-01292.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1292¶

X₁₂₉₂¶