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X₃₈₄₇¶

X₁₄₂₀com(3rd EULER TRIANGLE)

X₃₈₄₇ (X₁₄₂₀com(3rd EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3847 = X_1420com(3rd EULER 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,
            feuerbach_point_of,
            nagel_point_of,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03847(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3847 = X_1420com(3rd EULER TRIANGLE) on reference triangle ABC."""
            X_3847 = eval_barycentric_point(model, A, B, C, '(b + c - a)*(3*b**(3) + 3*c**(3) + 3*a*b**(2) + 3*a*c**(2) - 3*b**(2)*c - 3*b*c**(2) - 4*a*b*c)', ID="X_3847", classes=["selected", "target"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            central_line(model, X_8, X_11, 8, 11, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_515 = eval_trilinear_point(model, A, B, C, '(b + c)*sec(A) - b*sec(B) - c*sec(C)', ID="X_515", classes=["center", "incident"])
            central_line(model, X_5, X_515, 5, 515, incident=True)
            X_1698 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) + cos(A) - cos(B) - cos(C) + 1', ID="X_1698", classes=["center", "incident"])
            X_1706 = eval_trilinear_point(model, A, B, C, '(b*c*(2*(b + c) - a*(cos(A) - cos(B) - cos(C) + 1)))', ID="X_1706", classes=["center", "incident"])
            central_line(model, X_1698, X_1706, 1698, 1706, incident=True)
            return promote_point_to_top(model, X_3847)


        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_3847 on the given reference triangle."""
            model = create_model('X_3847 = X_1420com(3rd EULER TRIANGLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03847(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-03847.json"))
            write_center_svg(
                model_acute,
                here / "x-03847.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3847¶

X₃₈₄₇¶