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X₁₃₀₀¶

COLLINGS TRANSFORM OF X₁₃₆

X₁₃₀₀ (COLLINGS TRANSFORM OF X₁₃₆) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1300 = COLLINGS TRANSFORM OF X_136."""

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


        def construct_x_01300(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1300 = COLLINGS TRANSFORM OF X_136 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_186 = eval_trilinear_point(model, A, B, C, '4*cos(A) - sec(A)', ID="X_186", classes=["center"])
            X_1300 = cevapoint(model, A, B, C, X_4, X_186, ID="X_1300", classes=["selected", "target"])
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            central_line(model, X_4, X_110, 4, 110, incident=True)
            X_24 = eval_trilinear_point(model, A, B, C, 'sec(A)*cos(2*A)', ID="X_24", classes=["center", "incident"])
            X_107 = eval_trilinear_point(model, A, B, C, '1/(cos(A)*(sin(2*B) - sin(2*C)))', ID="X_107", classes=["center", "incident"])
            central_line(model, X_24, X_107, 24, 107, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_131 = point_from_barycentrics(model, A, B, C, 0.57236082, 0.12379803, 0.30384114, ID="X_131", classes=["center", "incident"])
            central_line(model, X_2, X_131, 2, 131, incident=True)
            return promote_point_to_top(model, X_1300)


        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_1300 on the given reference triangle."""
            model = create_model('X_1300 = COLLINGS TRANSFORM OF X_136')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01300(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-01300.json"))
            write_center_svg(
                model_acute,
                here / "x-01300.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1300¶

X₁₃₀₀¶