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X₃₇₁₈¶

X₁₇₁₆com(EXTOUCH TRIANGLE)

X₃₇₁₈ = excentral-to-ABC barycentric image of X₁₇₁₆

X₃₇₁₈ (X₁₇₁₆com(EXTOUCH TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3718 = X_1716com(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,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03718(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3718 = X_1716com(EXTOUCH TRIANGLE) on reference triangle ABC."""
            X_1395 = eval_trilinear_point(model, A, B, C, '(sin(A)*tan(A)*(sin(A/2))**(2))', ID="X_1395", classes=["center"])
            X_3718 = isogonal_conjugate(model, A, B, C, X_1395, ID="X_3718", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_75 = eval_trilinear_point(model, A, B, C, '1/a**(2)', ID="X_75", classes=["center", "incident"])
            central_line(model, X_10, X_75, 10, 75, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            central_line(model, X_69, X_72, 69, 72, incident=True)
            X_9 = mittenpunkt_of(model, A, B, C, ID="X_9", classes=["center", "incident"])
            X_312 = eval_trilinear_point(model, A, B, C, '(b + c - a)*b**(2)*c**(2)', ID="X_312", classes=["center", "incident"])
            central_line(model, X_9, X_312, 9, 312, incident=True)
            return promote_point_to_top(model, X_3718)


        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_3718 on the given reference triangle."""
            model = create_model('X_3718 = X_1716com(EXTOUCH TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03718(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-03718.json"))
            write_center_svg(
                model_acute,
                here / "x-03718.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3718¶

X₃₇₁₈¶