In the adjoining figure, if the radius of each of the four outer circles is `r` , what is the radius of the inner circle? (FIGURE) (a) `2/(sqrt(2)+1)r` (b) `1/(sqrt(2))r` (c) `(sqrt(2)-1)r` (d) `sqrt(2)\ r`

In the adjoining figure,if the radius of each of the four outer circles is r, what is the radius of the inner circle? (FIGURE) (a) (2)/(sqrt(2)+1)r(b)(1)/(sqrt(2))r(c)(sqrt(2)-1)r(d)sqrt(2)backslash r

The equation of four circles are (x+-a)^2+(y+-a)^2=a^2 . The radius of a circle touching all the four circles is (a) (sqrt(2)+2)a (b) 2sqrt(2)a (c) (sqrt(2)+1)a (d) (2+sqrt(2))a

The equation of four circles are (x+-a)^2+(y+-a)^2=a^2 . The radius of a circle touching all the four circles is (a) (sqrt(2)+2)a (b) 2sqrt(2)a (c) (sqrt(2)+1)a (d) (2+sqrt(2))a

A circle is circumscribed around a square as shown in the figure.The area of one of the four shaded portions is equal to (4)/(7). The radius of the circle is (FIGURE) sqrt(2)( b) (1)/(sqrt(2))(c)2(d)3

A circle S of radius ' a ' is the director circle of another circle S_1,S_1 is the director circle of circle S_2 and so on. If the sum of the radii of all these circle is 2, then the value of ' a ' is (a) 2+sqrt(2) (b) 2-1/(sqrt(2)) (c) 2-sqrt(2) (d) 2+1/(sqrt(2))

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

A B C D is a square of unit area. A circle is tangent to two sides of A B C D and passes through exactly one of its vertices. The radius of the circle is (a) 2-sqrt(2) (b) sqrt(2)-1 (c) sqrt(2)-1/2 (d) 1/(sqrt(2))

Three circles of radius 1 cm are circumscribed by a circle of radius r, as shown in the figure. Find the value of r? (a) sqrt(3) + 1 (b) (2+sqrt(3))/(sqrt(3)) (c) (sqrt(3) + 2)/(sqrt(2)) (d) 2 + sqrt(3)

The equation of four circles are (x+-a)^(2)+(y+-a^(2)=a^(2). The radius of a circle touching all the four circles is (sqrt(2)+2)a( b) 2sqrt(2)a(sqrt(2)+1)a(d)(2+sqrt(2))a

The largest area of the trapezium inscribed in a semi-circle or radius R , if the lower base is on the diameter, is (a) (3sqrt(3))/4R^2 (b) (sqrt(3))/2R^2 (c) (3sqrt(3))/8R^2 (d) R^2