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`

Consider four circles (x+-1)^2+(y+-1)^2=1 . Find the equation of the smaller circle touching these four circles.

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

The equation of a circle is x^2+y^2=4. Find the center of the smallest circle touching the circle and the line x+y=5sqrt(2)

The value of the definite integral int_0^(pi/2)sqrt(tanx)dx is (a) sqrt(2)pi (b) pi/(sqrt(2)) (c) 2sqrt(2)pi (d) pi/(2sqrt(2))

The equation of a circle of radius 1 touching the circle x^2 + y^2 - 2|x| = 0 is

The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|=0 is (a) x^2+y^2+2sqrt(2)x+1=0 (b) x^2+y^2-2sqrt(3)y+2=0 (c) x^2+y^2+2sqrt(3)y+2=0 (d) x^2+y^2-2sqrt(2)+1=0

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is (a) 2sqrt(3)-3 (b) 2sqrt(2)-1 (c) 2sqrt(2)-1 (d) 1

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))

Length of the latus rectum of the parabola sqrt(x) +sqrt(y) = sqrt(a) is (a) a sqrt(2) (b) (a)/(sqrt(2)) (c) a (d) 2a

The area enclosed by the curve y=sinx+cosxa n dy=|cosx-sinx| over the interval [0,pi/2] is (a)4(sqrt(2)-2) (b) 2sqrt(2) ( sqrt(2) -1) (c)2(sqrt(2) +1) (d) 2sqrt(2)(sqrt(2)+1)