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X₃₇₀₈¶

X₁₅₀com(EXTOUCH TRIANGLE)

X₃₇₀₈ = excentral-to-ABC barycentric image of X₁₅₀

X₃₇₀₈ (X₁₅₀com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3708 = X_150com(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,
            incenter_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03708(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3708 = X_150com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_3708 = eval_barycentric_point(model, A, B, C, '(a*(b**(2) - c**(2))**(2)*(b**(2) + c**(2) - a**(2)))', ID="X_3708", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_163 = eval_trilinear_point(model, A, B, C, '(sin(2*A))/(sin(2*B) - sin(2*C))', ID="X_163", classes=["center", "incident"])
            central_line(model, X_1, X_163, 1, 163, incident=True)
            X_115 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) - c**(2))**(2)', ID="X_115", classes=["center", "incident"])
            X_1365 = point_from_barycentrics(model, A, B, C, 0.14334182, 0.65139949, 0.20525869, ID="X_1365", classes=["center", "incident"])
            central_line(model, X_115, X_1365, 115, 1365, incident=True)
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            X_1146 = eval_trilinear_point(model, A, B, C, 'b*c*((b - c)*(b + c - a))**(2)', ID="X_1146", classes=["center", "incident"])
            central_line(model, X_523, X_1146, 523, 1146, incident=True)
            return promote_point_to_top(model, X_3708)


        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_3708 on the given reference triangle."""
            model = create_model('X_3708 = X_150com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03708(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-03708.json"))
            write_center_svg(
                model_acute,
                here / "x-03708.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3708¶

X₃₇₀₈¶