7 Two light inextensible strings each have one end attached to a particle, $P$, of mass 4 kg . The other ends of the strings are attached to the fixed points $A$ and $B$. The point $A$ is vertically above the point $B$.

The particle moves at a constant speed in a horizontal circle. The centre, $C$, of this circle is directly below the point $B$. The two strings are inclined at $30 ^ { \circ }$ and $50 ^ { \circ }$ to the vertical, as shown in the diagram. Both strings are taut.

As the particle moves in the horizontal circle, the tension in the string $B P$ is 20 N .\\
\includegraphics[max width=\textwidth, alt={}, center]{31ba38f7-38a8-4e4e-96a3-19e819fabfb0-5_750_469_742_781}
\begin{enumerate}[label=(\alph*)]
\item Find the tension in the string $A P$.
\item The speed of the particle is $5 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.

Find the length of $C P$, the radius of the horizontal circle.
\end{enumerate}

\hfill \mbox{\textit{AQA M2 2011 Q7 [8]}}