← etc / Encyclopedia of Triangle Centers

X₃₅₂¶

INVERSE-IN-CIRCUMCIRCLE OF X₃₅₃

X₃₅₂ = inverse-in-circumcircle of X₃₅₃

X₃₅₂ (INVERSE-IN-CIRCUMCIRCLE OF X₃₅₃) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_352 = INVERSE-IN-CIRCUMCIRCLE OF X_353."""

        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,
            circumcenter_of,
            construct_baseline_triangle,
            create_model,
            eval_trilinear_point,
            promote_point_to_top,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_00352(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_352 = INVERSE-IN-CIRCUMCIRCLE OF X_353 on reference triangle ABC."""
            X_352 = eval_trilinear_point(model, A, B, C, '(a*(-a**(4) - b**(4) - c**(4) - 5*b**(2)*c**(2) + 4*a**(2)*b**(2) + 4*a**(2)*c**(2)))', ID="X_352", classes=["selected", "target"])
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_2, X_6, 2, 6, incident=True)
            X_110 = eval_trilinear_point(model, A, B, C, 'csc(B - C)', ID="X_110", classes=["center", "incident"])
            X_187 = eval_trilinear_point(model, A, B, C, 'a*(2*a**(2) - b**(2) - c**(2))', ID="X_187", classes=["center", "incident"])
            central_line(model, X_110, X_187, 110, 187, incident=True)
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_353 = eval_trilinear_point(model, A, B, C, '(a*(4*a**(4) - 2*b**(4) - 2*c**(4) - b**(2)*c**(2) - 4*a**(2)*b**(2) -4*a**(2)*c**(2)))', ID="X_353", classes=["center", "incident"])
            central_line(model, X_3, X_353, 3, 353, incident=True)
            return promote_point_to_top(model, X_352)


        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_352 on the given reference triangle."""
            model = create_model('X_352 = INVERSE-IN-CIRCUMCIRCLE OF X_353')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_00352(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-00352.json"))
            write_center_svg(
                model_acute,
                here / "x-00352.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X352¶

X₃₅₂¶