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X₃₇₀₉¶

X₇₉₈com(EXTOUCH TRIANGLE)

X₃₇₀₉ = excentral-to-ABC barycentric image of X₇₉₈

X₃₇₀₉ (X₇₉₈com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3709 = X_798com(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,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03709(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3709 = X_798com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_3709 = eval_barycentric_point(model, A, B, C, '(a**(2)*(b + c - a)*(b**(2) - c**(2)))', ID="X_3709", classes=["selected", "target"])
            X_37 = eval_trilinear_point(model, A, B, C, 'b + c', ID="X_37", classes=["center", "incident"])
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            central_line(model, X_37, X_523, 37, 523, incident=True)
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            X_650 = eval_trilinear_point(model, A, B, C, 'cos(B) - cos(C)', ID="X_650", classes=["center", "incident"])
            central_line(model, X_522, X_650, 522, 650, incident=True)
            X_513 = eval_trilinear_point(model, A, B, C, 'b - c', ID="X_513", classes=["center", "incident"])
            X_665 = eval_trilinear_point(model, A, B, C, 'a*((a - b)**(2)*(a + b - c) - (c - a)**(2)*(c + a - b))', ID="X_665", classes=["center", "incident"])
            central_line(model, X_513, X_665, 513, 665, incident=True)
            return promote_point_to_top(model, X_3709)


        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_3709 on the given reference triangle."""
            model = create_model('X_3709 = X_798com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03709(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-03709.json"))
            write_center_svg(
                model_acute,
                here / "x-03709.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3709¶

X₃₇₀₉¶