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The diagram shows two congruent triangles, \(B C D\) and \(B A E\), where \(A B C\) is a straight line. In triangle \(B C D , B D = 8 \mathrm {~cm} , C D = 11 \mathrm {~cm}\) and angle \(C B D = 65 ^ { \circ }\). The points \(E\) and \(D\) are joined by an arc of a circle with centre \(B\) and radius 8 cm .
- Find angle \(B C D\).
- (a) Show that angle \(E B D\) is 0.873 radians, correct to 3 significant figures.
(b) Hence find the area of the shaded segment bounded by the chord \(E D\) and the arc \(E D\), giving your answer correct to 3 significant figures.