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X₃₅₅₆¶

INTERSECTION OF LINES X₂₅X_65 AND X₃₁X_56

X₃₅₅₆ (INTERSECTION OF LINES X₂₅X_65 AND X₃₁X_56) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3556 = INTERSECTION OF LINES X_25X_65 AND X_31X_56."""

        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,
            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_03556(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3556 = INTERSECTION OF LINES X_25X_65 AND X_31X_56 on reference triangle ABC."""
            X_63 = eval_trilinear_point(model, A, B, C, 'cot(A)', ID="X_63", classes=["center"])
            X_6 = symmedian_point_of(model, A, B, C, ID="X_6", classes=["center"])
            X_3556 = ceva_conjugate(model, A, B, C, X_63, X_6, ID="X_3556", classes=["selected", "target"])
            X_31 = eval_trilinear_point(model, A, B, C, 'a**(2)', ID="X_31", classes=["center", "incident"])
            X_56 = eval_trilinear_point(model, A, B, C, 'a/(b + c - a)', ID="X_56", classes=["center", "incident"])
            central_line(model, X_31, X_56, 31, 56, incident=True)
            X_25 = eval_trilinear_point(model, A, B, C, 'sin(A)*tan(A)', ID="X_25", classes=["center", "incident"])
            X_65 = eval_trilinear_point(model, A, B, C, 'cos(B) + cos(C)', ID="X_65", classes=["center", "incident"])
            central_line(model, X_25, X_65, 25, 65, incident=True)
            X_64 = eval_trilinear_point(model, A, B, C, '1/(cos(A) - cos(B)*cos(C))', ID="X_64", classes=["center", "incident"])
            X_71 = eval_trilinear_point(model, A, B, C, '(b + c)*cos(A)', ID="X_71", classes=["center", "incident"])
            central_line(model, X_64, X_71, 64, 71, incident=True)
            return promote_point_to_top(model, X_3556)


        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_3556 on the given reference triangle."""
            model = create_model('X_3556 = INTERSECTION OF LINES X_25X_65 AND X_31X_56')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03556(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-03556.json"))
            write_center_svg(
                model_acute,
                here / "x-03556.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3556¶

X₃₅₅₆¶