CAIE P3 (Pure Mathematics 3) 2018 June

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\includegraphics[max width=\textwidth, alt={}, center]{e835a60b-fbeb-49fb-ba6b-ac12c702d487-08_558_785_258_680} The diagram shows a kite \(O A B C\) in which \(A C\) is the line of symmetry. The coordinates of \(A\) and \(C\) are \(( 0,4 )\) and \(( 8,0 )\) respectively and \(O\) is the origin.

1. Find the equations of \(A C\) and \(O B\).
2. Find, by calculation, the coordinates of \(B\).

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\includegraphics[max width=\textwidth, alt={}, center]{e835a60b-fbeb-49fb-ba6b-ac12c702d487-10_499_922_262_607} The diagram shows a circle with centre \(O\) and radius \(r \mathrm {~cm}\). The points \(A\) and \(B\) lie on the circle and \(A T\) is a tangent to the circle. Angle \(A O B = \theta\) radians and \(O B T\) is a straight line.

1. Express the area of the shaded region in terms of \(r\) and \(\theta\).
2. In the case where \(r = 3\) and \(\theta = 1.2\), find the perimeter of the shaded region.