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X₃₈₇₀¶

X₂₈₈₆com[INVERSE(n(3rd EULER TRIANGLE))]

X₃₈₇₀ = perspector of Gemini triangle 29 and tangential triangle, wrt ABC, of {ABC, Gemini 29}-circumconic

X₃₈₇₀ (X₂₈₈₆com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3870 = X_2886com[INVERSE(n(3rd EULER TRIANGLE))]."""

        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_trilinear_point,
            incenter_of,
            isogonal_conjugate,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03870(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3870 = X_2886com[INVERSE(n(3rd EULER TRIANGLE))] on reference triangle ABC."""
            X_2191 = point_from_barycentrics(model, A, B, C, 0.42694064, 0.30136986, 0.2716895, ID="X_2191", classes=["center"])
            X_3870 = isogonal_conjugate(model, A, B, C, X_2191, ID="X_3870", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_55 = eval_trilinear_point(model, A, B, C, 'a*(b + c - a)', ID="X_55", classes=["center", "incident"])
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            central_line(model, X_55, X_63, 55, 63, incident=True)
            X_33 = eval_trilinear_point(model, A, B, C, '1 + sec(A)', ID="X_33", classes=["center", "incident"])
            X_92 = eval_trilinear_point(model, A, B, C, 'csc(2*A)', ID="X_92", classes=["center", "incident"])
            central_line(model, X_33, X_92, 33, 92, incident=True)
            return promote_point_to_top(model, X_3870)


        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_3870 on the given reference triangle."""
            model = create_model('X_3870 = X_2886com[INVERSE(n(3rd EULER TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03870(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-03870.json"))
            write_center_svg(
                model_acute,
                here / "x-03870.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3870¶

X₃₈₇₀¶