Three identical circles, each of radius $x$ , are drawn as shown in figure and tangent to a semicircle of radius $a$ , then $x$ in terms of $a$

Question

Three identical circles, each of radius $x$ , are drawn as shown in figure and tangent to a semicircle of radius $a$ , then $x$ in terms of $a$ ?

Smart Achievers · Accepted Answer

(3)

$From the diagram, ∠ A O B = ∠ B O C = ∠ C O D = 60 ° \Rightarrow ∠ Y O D = \frac{π}{6}$

$Let X be the centre of right-hand circle, O X \sin 30 ° = a$

$Now r = O Y = 2 a + a = a = \frac{r}{3}$

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