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X₃₆₃₅¶

H⁻¹(X₁₀; M, -1/2)

Recalling that triangle centers are functions, at (a,b,c) = (6,9,13), the values of X₃₆₃₅ and X₁₅₅₁₉ are equal.

X₃₆₃₅ (H⁻¹(X₁₀; M, -1/2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3635 = H⁻¹(X_10; M, -1/2)."""

        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_barycentric_point,
            eval_trilinear_point,
            incenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03635(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3635 = H⁻¹(X_10; M, -1/2) on reference triangle ABC."""
            X_3625 = eval_trilinear_point(model, A, B, C, 'b*c*(4*a - 3*b - 3*c)', ID="X_3625", classes=["center"])
            X_3635 = complement(model, A, B, C, X_3625, ID="X_3635", 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_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            X_3892 = eval_barycentric_point(model, A, B, C, '(a*(b**(3) + c**(3) - a**(2)*b - a**(2)*c - 6*a*b*c))', ID="X_3892", classes=["center", "incident"])
            central_line(model, X_65, X_3892, 65, 3892, incident=True)
            X_72 = eval_trilinear_point(model, A, B, C, '(b + c)*cot(A)', ID="X_72", classes=["center", "incident"])
            X_3898 = eval_barycentric_point(model, A, B, C, '(a*(b**(3) + c**(3) - a**(2)*b - a**(2)*c + 6*a*b*c))', ID="X_3898", classes=["center", "incident"])
            central_line(model, X_72, X_3898, 72, 3898, incident=True)
            return promote_point_to_top(model, X_3635)


        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_3635 on the given reference triangle."""
            model = create_model('X_3635 = H⁻¹(X_10; M, -1/2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03635(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-03635.json"))
            write_center_svg(
                model_acute,
                here / "x-03635.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3635¶

X₃₆₃₅¶