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X₁₄₅₉¶

X₅₂₁-BETH CONJUGATE OF X₅₂₁

X₁₄₅₉ = reflection of X₆₅₆ in X₉₀₅

X₁₄₅₉ (X₅₂₁-BETH CONJUGATE OF X₅₂₁) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_1459 = X_521-BETH CONJUGATE OF X_521."""

        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,
            incenter_of,
            promote_point_to_top,
            reflection_in_point,
            symmedian_point_of,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_01459(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_1459 = X_521-BETH CONJUGATE OF X_521 on reference triangle ABC."""
            X_656 = eval_trilinear_point(model, A, B, C, 'tan(B) - tan(C)', ID="X_656", classes=["center"])
            X_905 = eval_trilinear_point(model, A, B, C, '(b - c)*cot(A)', ID="X_905", classes=["center"])
            X_1459 = reflection_in_point(model, X_656, X_905, ID="X_1459", classes=["selected", "target"], guide=False)
            X_1 = incenter_of(model, A, B, C, ID="X_1", classes=["center", "incident"])
            X_522 = eval_trilinear_point(model, A, B, C, '(cos(B) - cos(C))*(csc(A))', ID="X_522", classes=["center", "incident"])
            central_line(model, X_1, X_522, 1, 522, incident=True)
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center", "incident"])
            X_657 = eval_trilinear_point(model, A, B, C, '(1 + cos(A))*(cos(B) - cos(C))', ID="X_657", classes=["center", "incident"])
            central_line(model, X_6, X_657, 6, 657, incident=True)
            X_242 = eval_trilinear_point(model, A, B, C, '((sec(A))*((sin(A))**(2) - sin(B)*sin(C)))', ID="X_242", classes=["center", "incident"])
            X_514 = eval_trilinear_point(model, A, B, C, '(b - c)/a', ID="X_514", classes=["center", "incident"])
            central_line(model, X_242, X_514, 242, 514, incident=True)
            return promote_point_to_top(model, X_1459)


        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_1459 on the given reference triangle."""
            model = create_model('X_1459 = X_521-BETH CONJUGATE OF X_521')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_01459(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-01459.json"))
            write_center_svg(
                model_acute,
                here / "x-01459.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X1459¶

X₁₄₅₉¶