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X₄₇₆¶

TIXIER POINT

The reflection of X₁₁₀ in the Euler line; X₄₇₆ is on the circumcircle. (Michel Tixier, 5/9/98). Also, X₄₇₆ is the center of the polar conic of X₃₀ with respect to the Neuberg cubic; this conic is a rectangular hyperbola passing through the incenter, the excenters, and X₃₀. (Peter Yff, 5/23/99)

X₄₇₆ (TIXIER POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_476 = TIXIER 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,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00476(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_476 = TIXIER POINT on reference triangle ABC."""
            X_476 = eval_trilinear_point(model, A, B, C, '1/((1 + 2*cos(2*A))*sin(B - C))', ID="X_476", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_74 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*cos(B)*cos(C))', ID="X_74", classes=["center", "incident"])
            central_line(model, X_30, X_74, 30, 74, incident=True)
            X_23 = eval_trilinear_point(model, A, B, C, 'a*(b**(4) + c**(4) - a**(4) - b**(2)*c**(2))', ID="X_23", classes=["center", "incident"])
            X_94 = eval_trilinear_point(model, A, B, C, 'csc(3*A)', ID="X_94", classes=["center", "incident"])
            central_line(model, X_23, X_94, 23, 94, incident=True)
            X_111 = eval_trilinear_point(model, A, B, C, 'a/(2*a**(2) - b**(2) - c**(2))', ID="X_111", classes=["center", "incident"])
            X_230 = eval_trilinear_point(model, A, B, C, 'b*c*(a**(2)*(2*a**(2) - b**(2) - c**(2)) + (b**(2) - c**(2))**(2))', ID="X_230", classes=["center", "incident"])
            central_line(model, X_111, X_230, 111, 230, incident=True)
            return promote_point_to_top(model, X_476)


        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_476 on the given reference triangle."""
            model = create_model('X_476 = TIXIER POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00476(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-00476.json"))
            write_center_svg(
                model_acute,
                here / "x-00476.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X476¶

X₄₇₆¶