← etc / Encyclopedia of Triangle Centers

X₂₆₁₆¶

POINT TANIA

X₂₆₁₆ (POINT TANIA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2616 = POINT TANIA."""

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


        def construct_x_02616(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2616 = POINT TANIA on reference triangle ABC."""
            X_2616 = eval_trilinear_point(model, A, B, C, 'tan(B - C)', ID="X_2616", classes=["selected", "target"])
            X_656 = eval_trilinear_point(model, A, B, C, 'tan(B) - tan(C)', ID="X_656", classes=["center", "incident"])
            X_1955 = eval_trilinear_point(model, A, B, C, '(sin(2*B)*sin(2*C) - (sin(2*A))**(2))', ID="X_1955", classes=["center", "incident"])
            central_line(model, X_656, X_1955, 656, 1955, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_2605 = eval_trilinear_point(model, A, B, C, '(sin(C- A) - sin(B - A))', ID="X_2605", classes=["center", "incident"])
            central_line(model, X_11, X_2605, 11, 2605, incident=True)
            X_523 = eval_trilinear_point(model, A, B, C, 'sin(B -C)', ID="X_523", classes=["center", "incident"])
            X_2594 = eval_trilinear_point(model, A, B, C, '(cos(C- A) + cos(B - A))', ID="X_2594", classes=["center", "incident"])
            central_line(model, X_523, X_2594, 523, 2594, incident=True)
            return promote_point_to_top(model, X_2616)


        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_2616 on the given reference triangle."""
            model = create_model('X_2616 = POINT TANIA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02616(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-02616.json"))
            write_center_svg(
                model_acute,
                here / "x-02616.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2616¶

X₂₆₁₆¶