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Q.

Three identical circles, each of radius a, are drawn as shown in figure and tangent to a semi circle of radius r, express a in terms of r?

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a

$\frac{r}{4}$

b

$\frac{r}{2}$

c

$\frac{r}{3}$

d

$\frac{2 r}{3}$

answer is C.

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Detailed Solution

detailed_solution_thumbnail

From the diagram, $∠ A O B = ∠ B O C = ∠ C O D = 60 °$
$\Rightarrow ∠ Y O D = \frac{π}{6}$
Question Image
$\Rightarrow$ Let X be the centre of right hand circle, $O X \sin 30 ° = a$
$\Rightarrow O X = 2 a$
Now $r = O Y = 2 a + a$

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