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X₁₄₅¶

ANTICOMPLEMENT OF NAGEL POINT

Let O_A be the circle tangent to side BC at its midpoint and to the circumcircle on the same side of BC as A. Define O_B, O_C cyclically. Then X₁₄₅ is the trilinear pole of the line of the exsimilicenters (the Monge line) of O_A, O_B, O_C. See the reference at X₁₀₀₁.

X₁₄₅ (ANTICOMPLEMENT OF NAGEL POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_145 = ANTICOMPLEMENT OF NAGEL 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,
            incenter_of,
            nagel_point_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00145(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_145 = ANTICOMPLEMENT OF NAGEL POINT on reference triangle ABC."""
            X_145 = eval_trilinear_point(model, A, B, C, 'b*c*(3*a - b - c)', ID="X_145", 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_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_8, X_1, 8, 1, incident=True)
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            X_100 = eval_trilinear_point(model, A, B, C, '1/(b - c)', ID="X_100", classes=["center", "incident"])
            central_line(model, X_56, X_100, 56, 100, incident=True)
            return promote_point_to_top(model, X_145)


        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_145 on the given reference triangle."""
            model = create_model('X_145 = ANTICOMPLEMENT OF NAGEL POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00145(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-00145.json"))
            write_center_svg(
                model_acute,
                here / "x-00145.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X145¶

X₁₄₅¶