As shown in the figure, three circles which have the same radius r,have centres at `(0,0);(1,1) and (2,1)`. If they have a common tangentline, as shown then, their radius 'r' is -

Find an equation of the circle with centre at (0,0) and radius r.

Find the equation of the circle with: centre (0,-1) and radius 1.

In the circuit shown in figure, the emfs of batteries are E_1 , and E_2 which have internal resistances R_1 , and R_2 . At what value of the resistance R will the thermal power generated in it be the highest? What it is?

In the figure, when the outer circles all have radii 'r', then the radius of the inner circle will be

Find the equation of the circles which touch 2x-3y+1=0 at (1,1) and having radius sqrt(13) .

The disc of radius r is confined to roll without slipping at A and B . If the plates have the velocities shown, then

If |z|lt1, then 1+2z lies (A) on or inside circle having center at origin and radius 2 (B) outside the circle having center at origin and radius 2 (C) inside the circle having center at (1,0) and radius 2 (D) outside the circle having center at (1,0) and radius 2.

Two identical circular wires P and Q each of radius R and carrying current 'I' are kept in perpendicular planes such that they have a common centre as shown in the figure. Find the magnitude and direction of the net magnetic field at the common centre of the two coils.

Two circles, each of radius 5, have a common tangent at (1, 1) whose equation is 3x+4y-7=0 . Then their centres, are