2. A metal sign is formed by removing triangle \(B C D\) from a rectangular lamina \(A C E F\) made of uniform material, and adding a quarter circle XYZ, made of the same uniform material, with a particle attached to its vertex at \(Y\). The sign is supported by two light chains fixed at \(E\) and \(F\). The quarter circle has radius 24 cm and the particle at \(Y\) has a mass equal to half of that of the removed triangle. \(X D\) is parallel to \(A C\) and \(B Z\) is parallel to \(A F\). The dimensions, in cm , are as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{3578a810-46da-4d9e-a98f-248be72a517a-3_885_636_712_715}

1. Calculate the distance of the centre of mass of the sign from
   1. \(A F\),
   2. \(A C\).
2. The support at \(F\) comes loose so that the sign is freely suspended at \(E\) by one chain alone. Given that it then hangs in equilibrium, calculate the angle that \(E F\) makes with the vertical.