Two circles of unit radius touch each other and each of them touches s internally touches a circle of radius two. Then the radius of the circle which touches all the three circles is :

Explanation

Let `C_1,C_2` are the centers of two small circles.
and `C` is the center of large circle.

Let `C_3` is the center and `r` is the radius of the circle that is touching these three circles.

Please refer to video for the diagram.

We can see that from the diagram, `Delta C C_1C_3` and `Delta C C_2C_3` will be right angle triangles.

`:. C_1C_3^2 = C C_3^2+C C_1^2`

From the given details,

`C C_1 = 1, C C_3 = 2-r, C_1 C_3 = 1+r`

`:. (1+r)^2 = (2-r)^2+1`

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