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X₃₅₃₁¶

INTERSECTION OF LINES X(3,373) AND X(69,381)

X₃₅₃₁ = perspector of circle (X₃,2R)

X₃₅₃₁ (INTERSECTION OF LINES X(3,373) AND X(69,381)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).¶

"""GEOMETOR construction model for X_3531 = INTERSECTION OF LINES X(3,373) AND X(69,381)."""

        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,
            isogonal_conjugate,
            promote_point_to_top,
        )
        from geometor.etc.render import write_center_svg


        def construct_x_03531(
            model: Model, A: spg.Point, B: spg.Point, C: spg.Point
        ) -> spg.Point:
            """Construct X_3531 = INTERSECTION OF LINES X(3,373) AND X(69,381) on reference triangle ABC."""
            X_3524 = eval_trilinear_point(model, A, B, C, '3*cos(A) + sin(B)*sin(C)', ID="X_3524", classes=["center"])
            X_3531 = isogonal_conjugate(model, A, B, C, X_3524, ID="X_3531", classes=["selected", "target"])
            X_3 = circumcenter_of(model, A, B, C, ID="X_3", classes=["center", "incident"])
            X_373 = eval_trilinear_point(model, A, B, C, '(2*b*c + a*c*cos(C) + a*b*cos(B))', ID="X_373", classes=["center", "incident"])
            central_line(model, X_3, X_373, 3, 373, incident=True)
            X_69 = eval_trilinear_point(model, A, B, C, '(cos(A))/a**(2)', ID="X_69", classes=["center", "incident"])
            X_381 = eval_trilinear_point(model, A, B, C, '2*cos(B - C) - cos(A)', ID="X_381", classes=["center", "incident"])
            central_line(model, X_69, X_381, 69, 381, incident=True)
            X_399 = eval_trilinear_point(model, A, B, C, '5*cos(A) - 4*cos(B)*cos(C) - 8*sin(B)*sin(C)*(cos(A))**(2)', ID="X_399", classes=["center", "incident"])
            X_895 = eval_trilinear_point(model, A, B, C, 'a*(b**(2) + c**(2) - a**(2))/(b**(2) + c**(2) - 2*a**(2))', ID="X_895", classes=["center", "incident"])
            central_line(model, X_399, X_895, 399, 895, incident=True)
            return promote_point_to_top(model, X_3531)


        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_3531 on the given reference triangle."""
            model = create_model('X_3531 = INTERSECTION OF LINES X(3,373) AND X(69,381)')
            A, B, C = construct_baseline_triangle(model, *sides, show_guides=show_guides)
            construct_x_03531(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-03531.json"))
            write_center_svg(
                model_acute,
                here / "x-03531.svg",
                subtitle="(a, b, c) = (5, 6, 7) | AB = 1",
            )
        

X3531¶

X₃₅₃₁¶