← etc / Encyclopedia of Triangle Centers

X₃₉₀₀¶

X₅₁₄com[INVERSE(n(3rd EULER TRIANGLE))]

X₃₉₀₀ = crossdifference of every pair of points on line X₆ X₅₇

X₃₉₀₀ (X₅₁₄com[INVERSE(n(3rd EULER TRIANGLE))]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3900 = X_514com[INVERSE(n(3rd EULER TRIANGLE))]."""

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


        def construct_x_03900(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3900 = X_514com[INVERSE(n(3rd EULER TRIANGLE))] on reference triangle ABC."""
            X_934 = eval_trilinear_point(model, A, B, C, '1/((b - c)*(b + c - a)**(2))', ID="X_934", classes=["center"])
            X_3900 = isogonal_conjugate(model, A, B, C, X_934, ID="X_3900", classes=["selected", "target"])
            X_30 = eval_trilinear_point(model, A, B, C, 'cos(A) - 2*cos(B)*cos(C)', ID="X_30", classes=["center", "incident"])
            X_511 = eval_trilinear_point(model, A, B, C, 'cos(A +  omega  )', ID="X_511", classes=["center", "incident"])
            central_line(model, X_30, X_511, 30, 511, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_885 = eval_barycentric_point(model, A, B, C, '(b - c)*(a - b - c)/(b**(2) + c**(2) - a*b - a*c)', ID="X_885", classes=["center", "incident"])
            central_line(model, X_8, X_885, 8, 885, incident=True)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_905 = eval_trilinear_point(model, A, B, C, '(b - c)*cot(A)', ID="X_905", classes=["center", "incident"])
            central_line(model, X_1, X_905, 1, 905, incident=True)
            return promote_point_to_top(model, X_3900)


        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_3900 on the given reference triangle."""
            model = create_model('X_3900 = X_514com[INVERSE(n(3rd EULER TRIANGLE))]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03900(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-03900.json"))
            write_center_svg(
                model_acute,
                here / "x-03900.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3900¶

X₃₉₀₀¶