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X₃₉₆₂¶

X₃₁₄₆com(EXTOUCH TRIANGLE)

X₃₉₆₂ (X₃₁₄₆com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3962 = X_3146com(EXTOUCH 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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03962(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3962 = X_3146com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_3962 = eval_barycentric_point(model, A, B, C, '(a*(b + c)*(3*b**(2) + 3*c**(2) - 3*a**(2) - 2*b*c))', ID="X_3962", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_12 = eval_trilinear_point(model, A, B, C, '1 + cos(B - C)', ID="X_12", classes=["center", "incident"])
            central_line(model, X_10, X_12, 10, 12, incident=True)
            X_144 = eval_trilinear_point(model, A, B, C, '(csc(A))*(tan(B/2) + tan(C/2) - tan(A/2))', ID="X_144", classes=["center", "incident"])
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", classes=["center", "incident"])
            central_line(model, X_144, X_145, 144, 145, incident=True)
            X_382 = eval_trilinear_point(model, A, B, C, 'cos(A) - 4*cos(B)*cos(C)', ID="X_382", classes=["center", "incident"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center", "incident"])
            central_line(model, X_382, X_517, 382, 517, incident=True)
            return promote_point_to_top(model, X_3962)


        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_3962 on the given reference triangle."""
            model = create_model('X_3962 = X_3146com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03962(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-03962.json"))
            write_center_svg(
                model_acute,
                here / "x-03962.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3962¶

X₃₉₆₂¶