← etc / Encyclopedia of Triangle Centers

X₃₅₃₄¶

EULER LINE INTERCEPT OF LINE X₁₅₄X_2777

X₃₅₃₄ = Stammler isogonal conjugate of X₆

X₃₅₃₄ (EULER LINE INTERCEPT OF LINE X₁₅₄X_2777) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3534 = EULER LINE INTERCEPT OF LINE X_154X_2777."""

        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_03534(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3534 = EULER LINE INTERCEPT OF LINE X_154X_2777 on reference triangle ABC."""
            X_3534 = eval_trilinear_point(model, A, B, C, '4*sec(A) - 5*sec(B)*sec(C)', ID="X_3534", 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_394 = eval_trilinear_point(model, A, B, C, 'cos(A)*cot(A)', ID="X_394", classes=["center", "incident"])
            X_399 = eval_trilinear_point(model, A, B, C, '5*cos(A) - 4*cos(B)*cos(C) - 8*sin(B)*sin(C)*(cos(A))**(2)', ID="X_399", classes=["center", "incident"])
            central_line(model, X_394, X_399, 394, 399, incident=True)
            X_542 = eval_barycentric_point(model, A, B, C, '2*a**(6) - 2*a**(4)*(b**(2) + c**(2)) + a**(2)*(b**(4) + c**(4)) - (b**(2) - c**(2))**(2)*(b**(2) + c**(2))', ID="X_542", classes=["center", "incident"])
            X_1350 = eval_trilinear_point(model, A, B, C, 'a - 4*R*cot(omega)*cos(A)', ID="X_1350", classes=["center", "incident"])
            central_line(model, X_542, X_1350, 542, 1350, incident=True)
            return promote_point_to_top(model, X_3534)


        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_3534 on the given reference triangle."""
            model = create_model('X_3534 = EULER LINE INTERCEPT OF LINE X_154X_2777')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03534(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-03534.json"))
            write_center_svg(
                model_acute,
                here / "x-03534.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3534¶

X₃₅₃₄¶