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\includegraphics[max width=\textwidth, alt={}, center]{028c7979-6b24-42d0-9857-c616a169b2b2-14_590_691_260_726} In the diagram, \(O A X B\) is a sector of a circle with centre \(O\) and radius 10 cm . The length of the chord \(A B\) is 12 cm . The line \(O X\) passes through \(M\), the mid-point of \(A B\), and \(O X\) is perpendicular to \(A B\). The shaded region is bounded by the chord \(A B\) and by the arc of a circle with centre \(X\) and radius \(X A\).

1. Show that angle \(A X B\) is 2.498 radians, correct to 3 decimal places.
2. Find the perimeter of the shaded region.
3. Find the area of the shaded region.