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X₁₂₈₉¶

COLLINGS TRANSFORM OF X₂₅

X₁₂₈₉ (COLLINGS TRANSFORM OF X₂₅) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1289 = COLLINGS TRANSFORM OF X_25."""

        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,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01289(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1289 = COLLINGS TRANSFORM OF X_25 on reference triangle ABC."""
            X_1289 = eval_trilinear_point(model, A, B, C, 'tan(A)*csc(B - C)/(sin(2*A) - tan(omega)  )', ID="X_1289", classes=["selected", "target"])
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center", "incident"])
            X_98 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  )', ID="X_98", classes=["center", "incident"])
            central_line(model, X_24, X_98, 24, 98, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_127 = eval_trilinear_point(model, A, B, C, 'b*c*(sin(2*B) - sin(2*C))*((b**(2) - c**(2))*sin(2*A) - b**(2)*sin(2*B) + c**(2)*sin(2*C))', ID="X_127", classes=["center", "incident"])
            central_line(model, X_4, X_127, 4, 127, incident=True)
            X_66 = eval_trilinear_point(model, A, B, C, 'b*c/(b**(4) + c**(4) - a**(4))', ID="X_66", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_66, X_74, 66, 74, incident=True)
            return promote_point_to_top(model, X_1289)


        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_1289 on the given reference triangle."""
            model = create_model('X_1289 = COLLINGS TRANSFORM OF X_25')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01289(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-01289.json"))
            write_center_svg(
                model_acute,
                here / "x-01289.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1289¶

X₁₂₈₉¶