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:

Explanation

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`

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