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X₃₇₆₇¶

X₃₀₅₃com[T(a², a² - c²)]

X₃₇₆₇ is the center of the inellipse that is the barycentric square of the orthic axis. The Brianchon point (perspector) of the inellipse is X₃₉₃. (Randy Hutson, October 15, 2018)

X₃₇₆₇ (X₃₀₅₃com[T(a², a² - c²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3767 = X_3053com[T(a², a² - c²)]."""

        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,
            construct_baseline_triangle,
            create_model,
            eval_barycentric_point,
            eval_trilinear_point,
            nine_point_center_of,
            orthocenter_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03767(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3767 = X_3053com[T(a², a² - c²)] on reference triangle ABC."""
            X_3767 = eval_barycentric_point(model, A, B, C, 'a**(4) + (b**(2) - c**(2))**(2)', ID="X_3767", classes=["selected", "target"])
            X_5 = nine_point_center_of(model, A, B, C, ID="X_5", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_5, X_6, 5, 6, incident=True)
            X_4 = orthocenter_of(model, A, B, C, ID="X_4", classes=["center", "incident"])
            X_32 = eval_trilinear_point(model, A, B, C, 'a**(3)', ID="X_32", classes=["center", "incident"])
            central_line(model, X_4, X_32, 4, 32, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_39 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2))', ID="X_39", classes=["center", "incident"])
            central_line(model, X_2, X_39, 2, 39, incident=True)
            return promote_point_to_top(model, X_3767)


        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_3767 on the given reference triangle."""
            model = create_model('X_3767 = X_3053com[T(a², a² - c²)]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03767(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-03767.json"))
            write_center_svg(
                model_acute,
                here / "x-03767.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3767¶

X₃₇₆₇¶