Three weightless rods of length \( l \) each are hinged at points \( A \) and \( B \) lying on t...

Three weightless rods of length \( l \) each are hinged at points \( A \) and \( B \) lying on the same horizontal and joint through hinges at points \( C \) and \( D \) (Fig. 45). The length \( A B=2 l \). A load of mass \( m \) is suspended at the hinge \( C \).
Determine the minimum force \( F_{\min } \) applied to the hinge \( D \) for which the middle rod remains horizontal.
Fig. 45