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X₁₆₇₀¶

INVERSE-IN-BROCARD-CIRCLE OF X₁₃₄₂

X₁₆₇₀ is the external center of similitude of the Gallatly circle and the 2nd Lemoine circle. (Peter J. C. Moses, 9/03; cf. X₁₃₄₂)

X₁₆₇₀ (INVERSE-IN-BROCARD-CIRCLE OF X₁₃₄₂) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1670 = INVERSE-IN-BROCARD-CIRCLE OF X_1342."""

        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,
            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_01670(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1670 = INVERSE-IN-BROCARD-CIRCLE OF X_1342 on reference triangle ABC."""
            X_1670 = eval_trilinear_point(model, A, B, C, 'sin(A) - cos(A)*cot( omega  /2)', ID="X_1670", 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_76 = eval_trilinear_point(model, A, B, C, '1/a**(3)', ID="X_76", classes=["center", "incident"])
            X_1677 = eval_trilinear_point(model, A, B, C, 'sec(A +  omega  /2)', ID="X_1677", classes=["center", "incident"])
            central_line(model, X_76, X_1677, 76, 1677, incident=True)
            X_262 = eval_trilinear_point(model, A, B, C, 'sec(A -  omega  )', ID="X_262", classes=["center", "incident"])
            X_1676 = eval_trilinear_point(model, A, B, C, 'csc(A +  omega  /2)', ID="X_1676", classes=["center", "incident"])
            central_line(model, X_262, X_1676, 262, 1676, incident=True)
            return promote_point_to_top(model, X_1670)


        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_1670 on the given reference triangle."""
            model = create_model('X_1670 = INVERSE-IN-BROCARD-CIRCLE OF X_1342')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01670(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-01670.json"))
            write_center_svg(
                model_acute,
                here / "x-01670.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1670¶

X₁₆₇₀¶