← etc / Encyclopedia of Triangle Centers

X₁₀₅₃¶

POINT ALHENA

X₁₀₅₃ (POINT ALHENA) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1053 = POINT ALHENA."""

        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_01053(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1053 = POINT ALHENA on reference triangle ABC."""
            X_238 = eval_trilinear_point(model, A, B, C, 'a**(2) - b*c', ID="X_238", classes=["center"])
            X_517 = eval_trilinear_point(model, A, B, C, '-1 + cos(B) + cos(C)', ID="X_517", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_1110 = eval_trilinear_point(model, A, B, C, '((a/(b - c))**(2))', ID="X_1110", classes=["center"])
            central_line(model, X_238, X_517, 238, 517)
            central_line(model, X_1, X_1110, 1, 1110)
            X_1053 = intersect_lines(model, X_238, X_517, X_1, X_1110, ID="X_1053", classes=["selected", "target"])
            X_905 = eval_trilinear_point(model, A, B, C, '(b - c)*cot(A)', ID="X_905", classes=["center", "incident"])
            X_1054 = eval_trilinear_point(model, A, B, C, 'b**(2) + c**(2) - a**(2) - 3*b*c + a*b + a*c', ID="X_1054", classes=["center", "incident"])
            central_line(model, X_905, X_1054, 905, 1054, incident=True)
            return promote_point_to_top(model, X_1053)


        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_1053 on the given reference triangle."""
            model = create_model('X_1053 = POINT ALHENA')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01053(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-01053.json"))
            write_center_svg(
                model_acute,
                here / "x-01053.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1053¶

X₁₀₅₃¶