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X₃₄₇₀¶

TRILINEAR PRODUCT X₇₄*X₁₇₄₉

X₃₄₇₀ (TRILINEAR PRODUCT X₇₄*X₁₇₄₉) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3470 = TRILINEAR PRODUCT X_74*X_1749."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            intersect_lines,
            nine_point_center_of,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03470(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3470 = TRILINEAR PRODUCT X_74*X_1749 on reference triangle ABC."""
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center"])
            X_1117 = eval_barycentric_point(model, A, B, C, '(a**(2)-a*b+b**(2)-c**(2))*(a**(2)+a*b+b**(2)-c**(2))*(a**(2)-b**(2)-a*c+c**(2))*(a**(2)-b**(2)+a*c+c**(2))*(a**(6)-a**(4)*b**(2)-a**(2)*b**(4)+b**(6)-3*a**(4)*c**(2)+a**(2)*b**(2)*c**(2)-3*b**(4)*c**(2)+3*a**(2)*c**(4)+3*b**(2)*c**(4)-c**(6))*(a**(6)-3*a**(4)*b**(2)+3*a**(2)*b**(4)-b**(6)-a**(4)*c**(2)+a**(2)*b**(2)*c**(2)+3*b**(4)*c**(2)-a**(2)*c**(4)-3*b**(2)*c**(4)+c**(6))*(a**(8)-4*a**(6)*b**(2)+6*a**(4)*b**(4)-4*a**(2)*b**(6)+b**(8)-4*a**(6)*c**(2)+a**(4)*b**(2)*c**(2)+a**(2)*b**(4)*c**(2)+2*b**(6)*c**(2)+6*a**(4)*c**(4)+a**(2)*b**(2)*c**(4)-6*b**(4)*c**(4)-4*a**(2)*c**(6)+2*b**(2)*c**(6)+c**(8))', ID="X_1117", classes=["center"])
            central_line(model, X_3, X_74, 3, 74)
            central_line(model, X_5, X_1117, 5, 1117)
            X_3470 = intersect_lines(model, X_3, X_74, X_5, X_1117, ID="X_3470", classes=["selected", "target"])
            X_1138 = eval_trilinear_point(model, A, B, C, '(1/(5*cos(A) - 4*cos(B)*cos(C) - 8*(cos(A))**(2)*sin(B)*sin(C)))', ID="X_1138", classes=["center", "incident"])
            X_2132 = point_from_barycentrics(model, A, B, C, -0.58419421, 0.77475873, 0.80943548, ID="X_2132", classes=["center", "incident"])
            central_line(model, X_1138, X_2132, 1138, 2132, incident=True)
            return promote_point_to_top(model, X_3470)


        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_3470 on the given reference triangle."""
            model = create_model('X_3470 = TRILINEAR PRODUCT X_74*X_1749')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03470(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-03470.json"))
            write_center_svg(
                model_acute,
                here / "x-03470.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3470¶

X₃₄₇₀¶