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X₃₈₆₅¶

PERSPECTOR OF ABC AND T(-bc, c²)

X₃₈₆₅ is the perspector of ABC and t(-bc, c²).

X₃₈₆₅ (PERSPECTOR OF ABC AND T(-bc, c²)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3865 = PERSPECTOR OF ABC AND T(-bc, c²)."""

        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_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03865(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3865 = PERSPECTOR OF ABC AND T(-bc, c²) on reference triangle ABC."""
            X_3865 = eval_barycentric_point(model, A, B, C, '(a*(b**(2) + a*c)*(c**(2) + a*b)*(b**(2) - b*c + c**(2)))', ID="X_3865", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_256 = eval_trilinear_point(model, A, B, C, '1/(a**(2) + b*c)', ID="X_256", classes=["center", "incident"])
            central_line(model, X_1, X_256, 1, 256, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_257 = eval_trilinear_point(model, A, B, C, '1/(a**(3) + a*b*c)', ID="X_257", classes=["center", "incident"])
            central_line(model, X_10, X_257, 10, 257, incident=True)
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_893 = eval_trilinear_point(model, A, B, C, 'a/(a**(2) + b*c)', ID="X_893", classes=["center", "incident"])
            central_line(model, X_39, X_893, 39, 893, incident=True)
            return promote_point_to_top(model, X_3865)


        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_3865 on the given reference triangle."""
            model = create_model('X_3865 = PERSPECTOR OF ABC AND T(-bc, c²)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03865(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-03865.json"))
            write_center_svg(
                model_acute,
                here / "x-03865.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3865¶

X₃₈₆₅¶