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 .
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1. Find the tension in the string \(A P\).
2. The speed of the particle is \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Find the length of \(C P\), the radius of the horizontal circle.