A circle with radius 2 is placed against a right angle. Another smaller circle is also placed as shown in the adjoining figure. What is the radius of the smaller circle?
Explanation:
AB = AK = 2
Quadrilateral ABCD is a square. ∴ AC = 2√2
⇒ KC = AC - AK = 2√2 - 2
Let the centre of the smaller circle be O and let its radius be x.
∴ OC = x√2 and KC = KO + OC = x + x√2
⇒ x + x√2 = 2√2 - 2
⇒ x = 22-21+2
⇒ x = (22-2)(1+2)×(2-1)(2-1) = 6 - 4√2
Hence, option (d).
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