Question 33

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waecmaths question: 

In the diagram, the two circles have a common a centre O, if the area of the larger circle is 100π and that of the smaller circle is 49 π. Find x 

Option A: 

2

Option B: 

3

Option C: 

4

Option D: 

5

waecmaths solution: 

$\begin{align}  & A=\pi r_{2}^{2}-\pi r_{1}^{2}=\pi (r_{2}^{2}-r_{1}^{2}) \\ & {{A}_{2}}=\pi r_{2}^{2}=100\pi c{{m}^{2}} \\ & r_{2}^{2}=100c{{m}^{2}},\text{ }{{r}_{2}}=10cm \\ & {{A}_{1}}=\pi r_{1}^{2}=49\pi  \\ & r_{1}^{2}=49c{{m}^{2}},\text{ }r=7cm \\ & x={{r}_{2}}-{{r}_{1}}=10cm-7cm=3cm \\\end{align}$

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