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 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

Simplify: (sqrt2 (2 + sqrt3))/(sqrt3 (sqrt3 + 1)) - (sqrt2 (2 - sqrt3))/(sqrt3 (sqrt3 -1))

The incenter of the triangle with vertices (1,sqrt(3)),(0,0), and (2,0) is (a) (1,(sqrt(3))/2) (b) (2/3,1/(sqrt(3))) (c) (2/3,(sqrt(3))/2) (d) (1,1/(sqrt(3)))

Find the angles of the triangle whose sides are (sqrt(3)+1)/(2sqrt(2)), (sqrt(3)-1)/(2sqrt(2)) and sqrt(3)/2 .

Values (s)(-i)^(1/3) is/are (sqrt(3)-i)/2 b. (sqrt(3)+i)/2 c. (-sqrt(3)-i)/2 d. (-sqrt(3)+i)/2

The locus of the mid-points of the chords of the circle of lines radiùs r which subtend an angle pi/4 at any point on the circumference of the circle is a concentric circle with radius equal to (a) (r)/(2) (b) (2r)/(3) (c) (r )/(sqrt(2)) (d) (r )/(sqrt(3))

Which of the following is equal to root(3)(-1) a. (sqrt(3)+sqrt(-1))/2 b. (-sqrt(3)+sqrt(-1))/(sqrt(-4)) c. (sqrt(3)-sqrt(-1))/(sqrt(-4)) d. -sqrt(-1)

Simplify : (sqrt5+sqrt3)((3sqrt3)/(sqrt5+sqrt2)-sqrt5/(sqrt3+sqrt2))

On the line segment joining (1, 0) and (3, 0) , an equilateral triangle is drawn having its vertex in the fourth quadrant. Then the radical center of the circles described on its sides. (a) (3,-1/(sqrt(3))) (b) (3,-sqrt(3)) (c) (2,-1/sqrt(3)) (d) (2,-sqrt(3))

Simplify : sqrt5/(sqrt2+sqrt3)-(3sqrt3)/(sqrt2+sqrt5)+(2sqrt2)/(sqrt3+sqrt5)