← etc / Encyclopedia of Triangle Centers

X₃₅₄₄¶

EULER LINE INTERCEPT OF LINE X₆X_14842

X₃₅₄₄ (EULER LINE INTERCEPT OF LINE X₆X_14842) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3544 = EULER LINE INTERCEPT OF LINE X_6X_14842."""

        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_barycentric_point,
            eval_trilinear_point,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03544(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3544 = EULER LINE INTERCEPT OF LINE X_6X_14842 on reference triangle ABC."""
            X_3544 = eval_barycentric_point(model, A, B, C, 'a**(4) + 8*a**(2)*b**(2) - 9*b**(4) + 8*a**(2)*c**(2) + 18*b**(2)*c**(2) - 9*c**(4)', ID="X_3544", 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_3070 = eval_trilinear_point(model, A, B, C, 'sin(A) + 2*cos(B)*cos(C)', ID="X_3070", classes=["center", "incident"])
            X_3317 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - 2*sin(A))', ID="X_3317", classes=["center", "incident"])
            central_line(model, X_3070, X_3317, 3070, 3317, incident=True)
            X_3071 = eval_trilinear_point(model, A, B, C, 'sin(A) - 2*cos(B)*cos(C)', ID="X_3071", classes=["center", "incident"])
            X_3316 = eval_trilinear_point(model, A, B, C, '1/(cos(A) + 2*sin(A))', ID="X_3316", classes=["center", "incident"])
            central_line(model, X_3071, X_3316, 3071, 3316, incident=True)
            return promote_point_to_top(model, X_3544)


        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_3544 on the given reference triangle."""
            model = create_model('X_3544 = EULER LINE INTERCEPT OF LINE X_6X_14842')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03544(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-03544.json"))
            write_center_svg(
                model_acute,
                here / "x-03544.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3544¶

X₃₅₄₄¶