← etc / Encyclopedia of Triangle Centers

X₃₆₃₁¶

H⁻¹(X₆; M, -2)

X₃₆₃₁ = midpoint of X₆₉ and X₁₄₁

X₃₆₃₁ (H⁻¹(X₆; M, -2)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3631 = H⁻¹(X_6; 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,
            midpoint,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03631(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3631 = H⁻¹(X_6; M, -2) on reference triangle ABC."""
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center"])
            X_141 = eval_trilinear_point(model, A, B, C, 'b*c*(b**(2) + c**(2))', ID="X_141", classes=["center"])
            X_3631 = midpoint(model, X_69, X_141, ID="X_3631", classes=["selected", "target"], guide=False)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_320 = eval_trilinear_point(model, A, B, C, '(1 - 2*cos(A))/a**(2)', ID="X_320", classes=["center", "incident"])
            X_594 = eval_trilinear_point(model, A, B, C, '(b + c)**(2)/a', ID="X_594", classes=["center", "incident"])
            central_line(model, X_320, X_594, 320, 594, incident=True)
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", 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_511, X_546, 511, 546, incident=True)
            return promote_point_to_top(model, X_3631)


        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_3631 on the given reference triangle."""
            model = create_model('X_3631 = H⁻¹(X_6; M, -2)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03631(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-03631.json"))
            write_center_svg(
                model_acute,
                here / "x-03631.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3631¶

X₃₆₃₁¶