← etc / Encyclopedia of Triangle Centers

X₁₃₂₆¶

INVERSE-IN-CIRCUMCIRCLE OF X₅₈

X₁₃₂₆ = circumcircle-inverse of X₅₈

X₁₃₂₆ (INVERSE-IN-CIRCUMCIRCLE OF X₅₈) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1326 = INVERSE-IN-CIRCUMCIRCLE OF X_58."""

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


        def construct_x_01326(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1326 = INVERSE-IN-CIRCUMCIRCLE OF X_58 on reference triangle ABC."""
            X_741 = eval_trilinear_point(model, A, B, C, '(1/(a **(-2)*(b**(1) + c**(1)) - a**(0)*(b **(-1) + c **(-1))))', ID="X_741", classes=["center"])
            X_58 = eval_trilinear_point(model, A, B, C, 'a/(b + c)', ID="X_58", classes=["center"])
            X_1326 = ceva_conjugate(model, A, B, C, X_741, X_58, ID="X_1326", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            central_line(model, X_3, X_6, 3, 6, incident=True)
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_261 = eval_trilinear_point(model, A, B, C, '(((csc(A))*(sec(B/2 - C/2)))**(2))', ID="X_261", classes=["center", "incident"])
            central_line(model, X_10, X_261, 10, 261, incident=True)
            X_42 = eval_trilinear_point(model, A, B, C, 'a*(b + c)', ID="X_42", classes=["center", "incident"])
            X_593 = eval_trilinear_point(model, A, B, C, 'a/(b + c)**(2)', ID="X_593", classes=["center", "incident"])
            central_line(model, X_42, X_593, 42, 593, incident=True)
            return promote_point_to_top(model, X_1326)


        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_1326 on the given reference triangle."""
            model = create_model('X_1326 = INVERSE-IN-CIRCUMCIRCLE OF X_58')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01326(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-01326.json"))
            write_center_svg(
                model_acute,
                here / "x-01326.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1326¶

X₁₃₂₆¶