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X₃₅₉₇¶

2nd ODEHNAL POINT

Let M_A, M_B, M_C be the centers of the circles A″, B″, C″ used to construct X₃₅₉₆, respectively. Then the lines A-to-M_A, B-to-M_B, C-to-M_C concur in X₃₅₉₇. For more, see the reference and sketch at X₃₅₉₆.

X₃₅₉₇ (2nd ODEHNAL POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3597 = 2nd ODEHNAL POINT."""

        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,
            orthocenter_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03597(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3597 = 2nd ODEHNAL POINT on reference triangle ABC."""
            X_3597 = eval_trilinear_point(model, A, B, C, '(b*c/(a**(5) + a**(4)*(b + c) - a**(3)*(b - c)**(2) - a**(2)*(b + c)*(b**(2) + c**(2)) - 2*a*b*c*(b**(2) + b*c + c**(2)) - 2*b**(2)*c**(2)*(b + c)))', ID="X_3597", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_970 = eval_trilinear_point(model, A, B, C, 'a*(a**(3)*(b + c)**(2) + a*(a*b + a*c - 2*b*c)*(b**(2) + c**(2)) - b*c*(b**(3) + c**(3)) - a*(b**(4) + c**(4)) - (b**(5) + c**(5)))', ID="X_970", classes=["center", "incident"])
            central_line(model, X_2, X_970, 2, 970, incident=True)
            X_226 = eval_trilinear_point(model, A, B, C, '(csc(A))*(cos(B) + cos(C))', ID="X_226", classes=["center", "incident"])
            X_986 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + b*c + c**(2)) + b**(3) + c**(3))', ID="X_986", classes=["center", "incident"])
            central_line(model, X_226, X_986, 226, 986, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_2092 = eval_trilinear_point(model, A, B, C, '(a**(2)*(b + c)**(2) + a*(b + c)*(b**(2) + c**(2)))', ID="X_2092", classes=["center", "incident"])
            central_line(model, X_4, X_2092, 4, 2092, incident=True)
            return promote_point_to_top(model, X_3597)


        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_3597 on the given reference triangle."""
            model = create_model('X_3597 = 2nd ODEHNAL POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03597(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-03597.json"))
            write_center_svg(
                model_acute,
                here / "x-03597.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3597¶

X₃₅₉₇¶