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Question 28

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?

Solution
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Using pythagoras we can find diagonal of small square shown in fig. = 2*$$\sqrt2$$ . Now this is equal to 2 + r +  $$\sqrt2$$ *r. Equating we get r = $$6- 4 \sqrt{2}$$

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