A circle with radius `2` is placed against a right angle. A smaller circle is also placed as shown in the adjoining figure. The radius of the smaller circle is:

A circle with radius `2` is placed against a right angle. A smaller ci

1.	A circle with radius `2` is placed against a right angle. A smaller circle is also placed as shown in the adjoining figure. The radius of the smaller circle is:
Answer» Let the radius of the larger circle is `R` and radius of the smaller circle is `r`. We can create a diagram with the given details. Please refer to video for the diagram. From the diagram, we can say that, `R^2+R^2 = (R+2r)^2` `=>2R^2 = (R+2r)^2` `=>R+2r = sqrt2R` `=>2r = sqrt2R-R` `=> r = (R(sqrt2-1))/2` We are given, `R = 2`, `:. r = sqrt2 -1` So, radius of smaller circle will be `sqrt2-1`.

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