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X₃₆₃₄¶

H⁻¹(X₁₀; M, 2)

X₃₆₃₄ = centroid of ABCX₁₀

X₃₆₃₄ (H⁻¹(X₁₀; M, 2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3634 = H⁻¹(X_10; M, 2)."""

        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,
            centroid_of,
            complement,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03634(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3634 = H⁻¹(X_10; M, 2) on reference triangle ABC."""
            X_1125 = eval_trilinear_point(model, A, B, C, '(2*a+b+c)/a', ID="X_1125", classes=["center"])
            X_3634 = complement(model, A, B, C, X_1125, ID="X_3634", classes=["selected", "target"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            central_line(model, X_1, X_2, 1, 2, incident=True)
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_516 = eval_trilinear_point(model, A, B, C, 'b*c*((a - b)*cot(C) + (a - c)*cot(B))', ID="X_516", classes=["center", "incident"])
            central_line(model, X_5, X_516, 5, 516, incident=True)
            X_140 = eval_trilinear_point(model, A, B, C, '2*cos(A) + cos(B - C)', ID="X_140", 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_140, X_515, 140, 515, incident=True)
            return promote_point_to_top(model, X_3634)


        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_3634 on the given reference triangle."""
            model = create_model('X_3634 = H⁻¹(X_10; M, 2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03634(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-03634.json"))
            write_center_svg(
                model_acute,
                here / "x-03634.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3634¶

X₃₆₃₄¶