← etc / Encyclopedia of Triangle Centers

X₃₇₇₉¶

X₃₀₅₆com[T(-bc, b²)]

X₃₇₇₉ = homothetic center of extangents triangle and reflection of intangents triangle in X₆

X₃₇₇₉ (X₃₀₅₆com[T(-bc, b²)]) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3779 = X_3056com[T(-bc, b²)]."""

        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,
            gergonne_point_of,
            nagel_point_of,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03779(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3779 = X_3056com[T(-bc, b²)] on reference triangle ABC."""
            X_3779 = eval_barycentric_point(model, A, B, C, 'a**(2)*(b**(3) + c**(3) - a*b**(2) - a*c**(2) - a*b*c)', ID="X_3779", classes=["selected", "target"])
            X_7 = gergonne_point_of(model, A, B, C, ID="X_7", classes=["center", "incident"])
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            central_line(model, X_7, X_8, 7, 8, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            central_line(model, X_6, X_31, 6, 31, incident=True)
            X_181 = eval_trilinear_point(model, A, B, C, 'a*(b + c)**(2)/(b + c - a)', ID="X_181", classes=["center", "incident"])
            X_200 = eval_trilinear_point(model, A, B, C, '(cot(A/2))**(2)', ID="X_200", classes=["center", "incident"])
            central_line(model, X_181, X_200, 181, 200, incident=True)
            return promote_point_to_top(model, X_3779)


        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_3779 on the given reference triangle."""
            model = create_model('X_3779 = X_3056com[T(-bc, b²)]')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03779(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-03779.json"))
            write_center_svg(
                model_acute,
                here / "x-03779.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3779¶

X₃₇₇₉¶