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X₁₉₈₅¶

EULER LINE INTERCEPT OF LINE X₆X_11

X₁₉₈₅ = inverse-in-orthocentroidal-circle of X₈₅₁

X₁₉₈₅ (EULER LINE INTERCEPT OF LINE X₆X_11) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1985 = EULER LINE INTERCEPT OF LINE X_6X_11."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01985(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1985 = EULER LINE INTERCEPT OF LINE X_6X_11 on reference triangle ABC."""
            X_1985 = eval_trilinear_point(model, A, B, C, '(sec(A) + sec(B) + sec(C))*csc(A) + (csc(A) + csc(B) + csc(C))*sec(A)', ID="X_1985", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_6, X_11, 6, 11, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_1837 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - 2*cos(B)*cos(C)', ID="X_1837", classes=["center", "incident"])
            central_line(model, X_42, X_1837, 42, 1837, incident=True)
            return promote_point_to_top(model, X_1985)


        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_1985 on the given reference triangle."""
            model = create_model('X_1985 = EULER LINE INTERCEPT OF LINE X_6X_11')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01985(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-01985.json"))
            write_center_svg(
                model_acute,
                here / "x-01985.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1985¶

X₁₉₈₅¶