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X₁₆₈₁¶

EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE)

X₁₆₈₁ is the exsimilicenter(1st Lemoine circle, Spieker circle).

X₁₆₈₁ (EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE)."""

        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_trilinear_point,
            nagel_point_of,
            promote_point_to_top,
            spieker_center_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01681(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE) on reference triangle ABC."""
            X_1681 = eval_trilinear_point(model, A, B, C, '(b*c*(b + c - a*cos(A -  omega  )))', ID="X_1681", classes=["selected", "target"])
            X_10 = spieker_center_of(model, A, B, C, ID="X_10", classes=["center", "incident"])
            X_182 = eval_trilinear_point(model, A, B, C, 'cos(A-  omega  )', ID="X_182", classes=["center", "incident"])
            central_line(model, X_10, X_182, 10, 182, incident=True)
            X_2 = centroid_of(model, A, B, C, ID="X_2", classes=["center", "incident"])
            X_1672 = eval_trilinear_point(model, A, B, C, '1 + cos(A -  omega  )', ID="X_1672", classes=["center", "incident"])
            central_line(model, X_2, X_1672, 2, 1672, incident=True)
            X_8 = nagel_point_of(model, A, B, C, ID="X_8", classes=["center", "incident"])
            X_1673 = eval_trilinear_point(model, A, B, C, '1 - cos(A -  omega  )', ID="X_1673", classes=["center", "incident"])
            central_line(model, X_8, X_1673, 8, 1673, incident=True)
            return promote_point_to_top(model, X_1681)


        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_1681 on the given reference triangle."""
            model = create_model('X_1681 = EXSIMILICENTER(1st LEMOINE CIRCLE, SPIEKER CIRCLE)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01681(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-01681.json"))
            write_center_svg(
                model_acute,
                here / "x-01681.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1681¶

X₁₆₈₁¶