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X₃₇₁₆¶

X₆₅₉com(EXTOUCH TRIANGLE)

X₃₇₁₆ (X₆₅₉com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3716 = X_659com(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,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            feuerbach_point_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03716(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3716 = X_659com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_2254 = eval_trilinear_point(model, A, B, C, '(b - c)*(a*b + a*c - b**(2) - c**(2))', ID="X_2254", classes=["center"])
            X_3716 = complement(model, A, B, C, X_2254, ID="X_3716", classes=["selected", "target"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_124 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - a)*(b - c)**(2)*((b + c)*(b**(2) + c**(2) - a**(2) - b*c) + a*b*c))', ID="X_124", classes=["center", "incident"])
            central_line(model, X_11, X_124, 11, 124, incident=True)
            X_118 = point_from_barycentrics(model, A, B, C, 0.28918651, -0.056547619, 0.76736111, ID="X_118", classes=["center", "incident"])
            X_120 = eval_trilinear_point(model, A, B, C, 'b*c*(2*a*b*c - (b + c)*(a**(2) + (b - c)**(2)))*(b**(2) + c**(2) - a*b -a*c)', ID="X_120", classes=["center", "incident"])
            central_line(model, X_118, X_120, 118, 120, 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)
            return promote_point_to_top(model, X_3716)


        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_3716 on the given reference triangle."""
            model = create_model('X_3716 = X_659com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03716(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-03716.json"))
            write_center_svg(
                model_acute,
                here / "x-03716.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3716¶

X₃₇₁₆¶