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X₃₆₉₂¶

X₁₇₂₃com(EXTOUCH TRIANGLE)

X₃₆₉₂ (X₁₇₂₃com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3692 = X_1723com(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_trilinear_point,
            isogonal_conjugate,
            mittenpunkt_of,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03692(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3692 = X_1723com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_1435 = eval_trilinear_point(model, A, B, C, '(tan(A)*(tan(A/2))**(2))', ID="X_1435", classes=["center"])
            X_3692 = isogonal_conjugate(model, A, B, C, X_1435, ID="X_3692", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            central_line(model, X_8, X_9, 8, 9, incident=True)
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center", "incident"])
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            central_line(model, X_63, X_69, 63, 69, incident=True)
            X_78 = eval_trilinear_point(model, A, B, C, '1/(1 - sec(A))', ID="X_78", classes=["center", "incident"])
            X_219 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A/2)', ID="X_219", classes=["center", "incident"])
            central_line(model, X_78, X_219, 78, 219, incident=True)
            return promote_point_to_top(model, X_3692)


        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_3692 on the given reference triangle."""
            model = create_model('X_3692 = X_1723com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03692(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-03692.json"))
            write_center_svg(
                model_acute,
                here / "x-03692.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3692¶

X₃₆₉₂¶