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X₁₈₆₅¶

ZOSMA TRANSFORM OF X₂₈₄

X₁₈₆₅ (ZOSMA TRANSFORM OF X₂₈₄) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1865 = ZOSMA TRANSFORM OF X_284."""

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


        def construct_x_01865(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1865 = ZOSMA TRANSFORM OF X_284 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_1859 = eval_trilinear_point(model, A, B, C, 'tan(A)*((b + c)*cos(A) + b*cos(B) + c*cos(C))', ID="X_1859", classes=["center"])
            X_1865 = ceva_conjugate(model, A, B, C, X_4, X_1859, ID="X_1865", classes=["selected", "target"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_4, X_6, 4, 6, incident=True)
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            central_line(model, X_12, X_37, 12, 37, incident=True)
            X_19 = eval_trilinear_point(model, A, B, C, 'tan(A)', ID="X_19", classes=["center", "incident"])
            X_407 = point_from_barycentrics(model, A, B, C, 0.10813862, 0.19355731, 0.69830407, ID="X_407", classes=["center", "incident"])
            central_line(model, X_19, X_407, 19, 407, incident=True)
            return promote_point_to_top(model, X_1865)


        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_1865 on the given reference triangle."""
            model = create_model('X_1865 = ZOSMA TRANSFORM OF X_284')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01865(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-01865.json"))
            write_center_svg(
                model_acute,
                here / "x-01865.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1865¶

X₁₈₆₅¶