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X₁₄₆₁¶

X₆₅₁-BETH CONJUGATE OF X₆₅₁

X₁₄₆₁ = barycentric product of circumcircle intercepts of the Soddy line

X₁₄₆₁ (X₆₅₁-BETH CONJUGATE OF X₆₅₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1461 = X_651-BETH CONJUGATE OF X_651."""

        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_trilinear_point,
            intersect_lines,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01461(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1461 = X_651-BETH CONJUGATE OF X_651 on reference triangle ABC."""
            X_77 = eval_trilinear_point(model, A, B, C, '1/(1 + sec(A))', ID="X_77", classes=["center"])
            X_572 = eval_trilinear_point(model, A, B, C, '(cos(A - U))', ID="X_572", classes=["center"])
            X_101 = eval_trilinear_point(model, A, B, C, 'a/(b - c)', ID="X_101", classes=["center"])
            X_651 = eval_trilinear_point(model, A, B, C, '1/(cos(B) - cos(C))', ID="X_651", classes=["center"])
            central_line(model, X_77, X_572, 77, 572)
            central_line(model, X_101, X_651, 101, 651)
            X_1461 = intersect_lines(model, X_77, X_572, X_101, X_651, ID="X_1461", classes=["selected", "target"])
            X_109 = eval_trilinear_point(model, A, B, C, 'a/(cos(B) - cos(C))', ID="X_109", classes=["center", "incident"])
            X_692 = eval_trilinear_point(model, A, B, C, 'a**(2)/(b - c)', ID="X_692", classes=["center", "incident"])
            central_line(model, X_109, X_692, 109, 692, incident=True)
            return promote_point_to_top(model, X_1461)


        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_1461 on the given reference triangle."""
            model = create_model('X_1461 = X_651-BETH CONJUGATE OF X_651')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01461(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-01461.json"))
            write_center_svg(
                model_acute,
                here / "x-01461.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1461¶

X₁₄₆₁¶