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Problem 229
229
In the diagram, \(OAXB\) is a sector of a circle with centre \(O\) and radius 10 cm. The length of the chord \(AB\) is 12 cm. The line \(OX\) passes through \(M\), the mid-point of \(AB\), and \(OX\) is perpendicular to \(AB\). The shaded region is bounded by the chord \(AB\) and by the arc of a circle with centre \(X\) and radius \(XA\).
(i) Show that angle \(AXB\) is 2.498 radians, correct to 3 decimal places.
(ii) Find the perimeter of the shaded region.
(iii) Find the area of the shaded region.
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