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\includegraphics[max width=\textwidth, alt={}, center]{4782d612-0ec1-418e-8ef3-c871dce82b44-10_611_732_255_705} The diagram shows two circles with centres \(A\) and \(B\) having radii 8 cm and 10 cm respectively. The two circles intersect at \(C\) and \(D\) where \(C A D\) is a straight line and \(A B\) is perpendicular to \(C D\).

1. Find angle \(A B C\) in radians.
2. Find the area of the shaded region.
   \(8 \quad A ( - 1,1 )\) and \(P ( a , b )\) are two points, where \(a\) and \(b\) are constants. The gradient of \(A P\) is 2 .
3. Find an expression for \(b\) in terms of \(a\).
4. \(B ( 10 , - 1 )\) is a third point such that \(A P = A B\). Calculate the coordinates of the possible positions of \(P\).