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?


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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