← etc / Encyclopedia of Triangle Centers

X₃₆₁₅¶

2nd HUTSON-FEUERBACH POINT

X₃₆₁₅ (2nd HUTSON-FEUERBACH POINT) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3615 = 2nd HUTSON-FEUERBACH POINT."""

        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,
            feuerbach_point_of,
            isogonal_conjugate,
            nine_point_center_of,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03615(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3615 = 2nd HUTSON-FEUERBACH POINT on reference triangle ABC."""
            X_2594 = eval_trilinear_point(model, A, B, C, '(cos(C- A) + cos(B - A))', ID="X_2594", classes=["center"])
            X_3615 = isogonal_conjugate(model, A, B, C, X_2594, ID="X_3615", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_49 = eval_trilinear_point(model, A, B, C, 'cos(3*A)', ID="X_49", classes=["center", "incident"])
            central_line(model, X_5, X_49, 5, 49, incident=True)
            X_21 = eval_trilinear_point(model, A, B, C, '1/(cos(B) + cos(C))', ID="X_21", classes=["center", "incident"])
            X_36 = eval_trilinear_point(model, A, B, C, '1 - 2*cos(A)', ID="X_36", classes=["center", "incident"])
            central_line(model, X_21, X_36, 21, 36, incident=True)
            X_11 = feuerbach_point_of(model, A, B, C, ID="X_11", classes=["center", "incident"])
            X_60 = eval_trilinear_point(model, A, B, C, '1/(1 + cos(B - C))', ID="X_60", classes=["center", "incident"])
            central_line(model, X_11, X_60, 11, 60, incident=True)
            return promote_point_to_top(model, X_3615)


        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_3615 on the given reference triangle."""
            model = create_model('X_3615 = 2nd HUTSON-FEUERBACH POINT')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03615(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-03615.json"))
            write_center_svg(
                model_acute,
                here / "x-03615.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3615¶

X₃₆₁₅¶