Geometry & Shapes (id: 1bb007cb6)

本题目来源于试卷: Geometry & Shapes，类别为 IB数学

[问答题]
The diagram below shows twx*fw-kz.m sw4 o cirycmjav9a7z 5fe pbs tsfvj 012*d5i 56cles with centres at the points A and B and radii 3r and 2r, respectively. The point B lies on the circle with centre A. The circl5ecmz 5dfbvtpv709 *y ssfj ai256j1aes intersect at the points C and D.



Let $\alpha$ be the measure of the angle CAD and $\theta $ be the measure of the angle CBD in radians.
1. Find an expression for the shaded area in terms of $ \alpha, \theta$ and r .
2. Show that $ \alpha=4 \arcsin \frac{1}{3}$ .
3. Hence find the value of r given that the shaded area is equal to 16 $\mathrm{~cm}^{2}$ .

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