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X₁₈₆₃¶

ZOSMA TRANSFORM OF X₂₆₉

X₁₈₆₃ (ZOSMA TRANSFORM OF X₂₆₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1863 = ZOSMA TRANSFORM OF X_269."""

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


        def construct_x_01863(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1863 = ZOSMA TRANSFORM OF X_269 on reference triangle ABC."""
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center"])
            X_1851 = point_from_barycentrics(model, A, B, C, 0.076660459, 0.18621974, 0.7371198, ID="X_1851", classes=["center"])
            X_1863 = ceva_conjugate(model, A, B, C, X_4, X_1851, ID="X_1863", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_4, X_7, 4, 7, incident=True)
            X_33 = eval_trilinear_point(model, A, B, C, '1 + sec(A)', ID="X_33", classes=["center", "incident"])
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            central_line(model, X_33, X_42, 33, 42, incident=True)
            X_242 = eval_trilinear_point(model, A, B, C, '((sec(A))*((sin(A))**(2) - sin(B)*sin(C)))', ID="X_242", classes=["center", "incident"])
            X_390 = eval_trilinear_point(model, A, B, C, 'b*c*(b + c - a)*(3*a**(2) + (b - c)**(2))', ID="X_390", classes=["center", "incident"])
            central_line(model, X_242, X_390, 242, 390, incident=True)
            return promote_point_to_top(model, X_1863)


        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_1863 on the given reference triangle."""
            model = create_model('X_1863 = ZOSMA TRANSFORM OF X_269')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01863(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-01863.json"))
            write_center_svg(
                model_acute,
                here / "x-01863.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1863¶

X₁₈₆₃¶