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X₃₇₈₂¶

X₂₈₈₇com[T(-bc, c²)]

X₃₇₈₂ = pole of de Longchamps line wrt incircle

X₃₇₈₂ (X₂₈₈₇com[T(-bc, c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3782 = X_2887com[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,
            centroid_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03782(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3782 = X_2887com[T(-bc, c²)] on reference triangle ABC."""
            X_3782 = eval_barycentric_point(model, A, B, C, '((b**(3) + c**(3) + a*b**(2) + a*c**(2) - b**(2)*c - c**(2)*b))', ID="X_3782", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            central_line(model, X_1, X_30, 1, 30, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_45 = eval_trilinear_point(model, A, B, C, '2*b + 2*c - a', ID="X_45", classes=["center", "incident"])
            central_line(model, X_2, X_45, 2, 45, incident=True)
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center", "incident"])
            X_321 = eval_trilinear_point(model, A, B, C, '(b + c)*b**(2)*c**(2)', ID="X_321", classes=["center", "incident"])
            central_line(model, X_141, X_321, 141, 321, incident=True)
            return promote_point_to_top(model, X_3782)


        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_3782 on the given reference triangle."""
            model = create_model('X_3782 = X_2887com[T(-bc, c²)]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03782(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-03782.json"))
            write_center_svg(
                model_acute,
                here / "x-03782.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3782¶

X₃₇₈₂¶