In the given figure, PQRS is a rectangle and a semicircle with SR as diameter is drawn. A circle is drawn as shown in the figure. If QR = 7 cm, then what is the radius (in cm) of the small circle?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 21 – 14√2
Radius of smaller circle = r
7 + r + r√2 = 7√2
⇒ r (√2 + 1) = 7 (√2 – 1)
⇒ r = 7 (√2 – 1)/(√2 – 1)
⇒
⇒ r 
⇒ r = 7 (3 – 2√2) = 21 – 14√2