← etc / Encyclopedia of Triangle Centers

X₂₁₃₄¶

EIGENTRANSFORM OF X₃₇

X₂₁₃₄ (EIGENTRANSFORM OF X₃₇) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_2134 = EIGENTRANSFORM OF X_37."""

        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_02134(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_2134 = EIGENTRANSFORM OF X_37 on reference triangle ABC."""
            X_81 = eval_trilinear_point(model, A, B, C, '1/(b + c)', ID="X_81", classes=["center"])
            X_763 = eval_trilinear_point(model, A, B, C, '(b + c) **(-3)', ID="X_763", classes=["center"])
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center"])
            X_1326 = eval_trilinear_point(model, A, B, C, '(a*(b**(2) + c**(2) - a**(2) + b*c - a*b - a*c)/(b + c))', ID="X_1326", classes=["center"])
            central_line(model, X_81, X_763, 81, 763)
            central_line(model, X_1, X_1326, 1, 1326)
            X_2134 = intersect_lines(model, X_81, X_763, X_1, X_1326, ID="X_2134", classes=["selected", "target"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            X_1931 = eval_trilinear_point(model, A, B, C, '(((b + c)**(2) - (a + b)*(a + c))/(b + c))', ID="X_1931", classes=["center", "incident"])
            central_line(model, X_39, X_1931, 39, 1931, incident=True)
            return promote_point_to_top(model, X_2134)


        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_2134 on the given reference triangle."""
            model = create_model('X_2134 = EIGENTRANSFORM OF X_37')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_02134(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-02134.json"))
            write_center_svg(
                model_acute,
                here / "x-02134.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X2134¶

X₂₁₃₄¶