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X₁₆₇¶

NAGEL POINT OF EXCENTRAL TRIANGLE

X₁₆₇ (NAGEL POINT OF EXCENTRAL TRIANGLE) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_167 = NAGEL POINT OF EXCENTRAL TRIANGLE."""

        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,
            incenter_of,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00167(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_167 = NAGEL POINT OF EXCENTRAL TRIANGLE on reference triangle ABC."""
            X_164 = eval_trilinear_point(model, A, B, C, 'sin(B/2) + sin(C/2) - sin(A/2)', ID="X_164", classes=["center"])
            X_165 = eval_trilinear_point(model, A, B, C, 'tan(B/2) + tan(C/2) - tan(A/2)', ID="X_165", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_174 = eval_trilinear_point(model, A, B, C, 'sec(A/2)', ID="X_174", classes=["center"])
            central_line(model, X_164, X_165, 164, 165)
            central_line(model, X_1, X_174, 1, 174)
            X_167 = intersect_lines(model, X_164, X_165, X_1, X_174, ID="X_167", classes=["selected", "target"])
            X_166 = eval_trilinear_point(model, A, B, C, '((tan(A/2))/(cos(B/2) + cos(C/2) - cos(A/2)) - (tan(B/2))/(cos(C/2) + cos(A/2) - cos(B/2)) - (tan(C/2))/(cos(A/2) + cos(B/2) - cos(C/2)))', ID="X_166", classes=["center", "incident"])
            X_188 = eval_trilinear_point(model, A, B, C, 'csc(A/2)', ID="X_188", classes=["center", "incident"])
            central_line(model, X_166, X_188, 166, 188, incident=True)
            return promote_point_to_top(model, X_167)


        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_167 on the given reference triangle."""
            model = create_model('X_167 = NAGEL POINT OF EXCENTRAL TRIANGLE')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00167(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-00167.json"))
            write_center_svg(
                model_acute,
                here / "x-00167.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X167¶

X₁₆₇¶