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X₃₆₃₆¶

H⁻¹(X₁₀; M, -2)

X₃₆₃₆ = midpoint of X₁ and X₁₁₂₅ (the anticomplement and complement of X₁₀)

X₃₆₃₆ (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_3636 = 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03636(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3636 = H⁻¹(X_10; M, -2) on reference triangle ABC."""
            X_3636 = eval_trilinear_point(model, A, B, C, 'b*c*(6*a + b + c)', ID="X_3636", 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_515 = eval_trilinear_point(model, A, B, C, '(b + c)*sec(A) - b*sec(B) - c*sec(C)', ID="X_515", classes=["center", "incident"])
            X_546 = eval_trilinear_point(model, A, B, C, '3*cos(B - C) - 2*cos(A)', ID="X_546", classes=["center", "incident"])
            central_line(model, X_515, X_546, 515, 546, incident=True)
            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"])
            X_550 = eval_trilinear_point(model, A, B, C, '- cos(B - C) + 4*cos(A)', ID="X_550", classes=["center", "incident"])
            central_line(model, X_516, X_550, 516, 550, incident=True)
            return promote_point_to_top(model, X_3636)


        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_3636 on the given reference triangle."""
            model = create_model('X_3636 = H⁻¹(X_10; M, -2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03636(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-03636.json"))
            write_center_svg(
                model_acute,
                here / "x-03636.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3636¶

X₃₆₃₆¶