← etc / Encyclopedia of Triangle Centers

X₄₅₃¶

POINT ALSHAIN

X₄₅₃ (POINT ALSHAIN) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_453 = POINT ALSHAIN."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            point_from_barycentrics,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00453(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_453 = POINT ALSHAIN on reference triangle ABC."""
            X_453 = eval_trilinear_point(model, A, B, C, '((cos(B) + cos(C) - cos(A))**(2)/(cos(B) + cos(C)))', ID="X_453", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center"])
            central_line(model, X_2, X_3, 2, 3)
            X_46 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C) - cos(A)', ID="X_46", classes=["center", "incident"])
            X_1800 = point_from_barycentrics(model, A, B, C, 0.052073717, 0.50162612, 0.44630016, ID="X_1800", classes=["center", "incident"])
            central_line(model, X_46, X_1800, 46, 1800, incident=True)
            X_1014 = eval_trilinear_point(model, A, B, C, '(1/((b + c)*(b + c - a)))', ID="X_1014", classes=["center", "incident"])
            X_1454 = point_from_barycentrics(model, A, B, C, 0.16822905, 0.28951384, 0.5422571, ID="X_1454", classes=["center", "incident"])
            central_line(model, X_1014, X_1454, 1014, 1454, incident=True)
            return promote_point_to_top(model, X_453)


        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_453 on the given reference triangle."""
            model = create_model('X_453 = POINT ALSHAIN')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00453(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-00453.json"))
            write_center_svg(
                model_acute,
                here / "x-00453.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X453¶

X₄₅₃¶