Points \(A,B,C\) lie on a circle with centre \(O\); \(A,B,D\) lie on another circle with centre \(P\).
Show that triangles ABC and ADB are similar, giving reasons.[2]
Given \(AC=6\) cm and \(CD=12\) cm, calculate \(AB\).[2]
A semicircle FBCE has centre O and radius 8 cm. AB and CD are tangents at B and C. A,F,O,E,D are collinear with AD=24 cm and AF=ED. Calculate the shaded area.[5]
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Answer:(a)(i) similar (AA) (ii) \(10.4\text{ cm}\) (b) \(17.7\text{ cm}^2\)