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In the diagram the lengths of \(A B\) and \(A C\) are both 15 cm . The point \(P\) is the foot of the perpendicular from \(C\) to \(A B\). The length \(C P = 9 \mathrm {~cm}\). An arc of a circle with centre \(B\) passes through \(C\) and meets \(A B\) at \(Q\).
- Show that angle \(A B C = 1.25\) radians, correct to 3 significant figures.
- Calculate the area of the shaded region which is bounded by the \(\operatorname { arc } C Q\) and the lines \(C P\) and \(P Q\).