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X₃₉₂₉¶

X₁₅₄com[INVERSE(n(EXTANGENTS TRIANGLE))]

X₃₉₂₉ = 2nd-extouch-to-excentral similarity image of X₂

X₃₉₂₉ (X₁₅₄com[INVERSE(n(EXTANGENTS TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3929 = X_154com[INVERSE(n(EXTANGENTS 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,
            gergonne_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03929(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3929 = X_154com[INVERSE(n(EXTANGENTS TRIANGLE))] on reference triangle ABC."""
            X_3929 = eval_trilinear_point(model, A, B, C, '(3*cot(A) + csc(A))', ID="X_3929", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            central_line(model, X_2, X_7, 2, 7, incident=True)
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_40 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A) - 1', ID="X_40", classes=["center", "incident"])
            central_line(model, X_30, X_40, 30, 40, incident=True)
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center", "incident"])
            X_210 = eval_trilinear_point(model, A, B, C, '(b + c)*(b + c - a)', ID="X_210", classes=["center", "incident"])
            central_line(model, X_165, X_210, 165, 210, incident=True)
            return promote_point_to_top(model, X_3929)


        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_3929 on the given reference triangle."""
            model = create_model('X_3929 = X_154com[INVERSE(n(EXTANGENTS TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03929(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-03929.json"))
            write_center_svg(
                model_acute,
                here / "x-03929.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3929¶

X₃₉₂₉¶