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In the diagram, \(X\) and \(Y\) are points on the line \(A B\) such that \(B X = 9 \mathrm {~cm}\) and \(A Y = 11 \mathrm {~cm}\). Arc \(B C\) is part of a circle with centre \(X\) and radius 9 cm , where \(C X\) is perpendicular to \(A B\). Arc \(A C\) is part of a circle with centre \(Y\) and radius 11 cm .
- Show that angle \(X Y C = 0.9582\) radians, correct to 4 significant figures.
- Find the perimeter of \(A B C\).