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

In the curve y=x^(3)+ax and y=bx^(2)+c pass through the point (-1,0) and have a common tangent line at this point then the value of a+b+c is

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

Find the equation of the circle with centre at (-1,0) and radius 2.

The centres of two circles C_(1) and C_(2) each of unit radius are at a distance of 6 unit from each other. Let P be the mid-point of the line segment joining the centres of C_(1) and C_(2) and C be a circle touching circles C_(1) and C_(2) externally. If a common tangent to C_(1) and C passing through P is also a common tangent to C_(2) and C, then the radius of the circle C, is

If the equations 2x^(2)-7x+1=0 and ax^(2)+bx+2=0 have a common root, then

Two circles with equal radii are intersecting at the points (0, 1) and (0,-1). The tangent at the point (0,1) to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is.

C_1 and C_2 are circle of unit radius with centers at (0, 0) and (1, 0), respectively, C_3 is a circle of unit radius. It passes through the centers of the circles C_1a n dC_2 and has its center above the x-axis. Find the equation of the common tangent to C_1a n dC_3 which does not pass through C_2dot

Let C_1 be the circle with center O_1(0,0) and radius 1 and C_2 be the circle with center O_2(t ,t^2+1),(t in R), and radius 2. Statement 1 : Circles C_1a n dC_2 always have at least one common tangent for any value of t Statement 2 : For the two circles O_1O_2geq|r_1-r_2|, where r_1a n dr_2 are their radii for any value of tdot

Let C be the circle with centre at (1,1) and radius =1 . If T is the circle centered at (0,y) passing through the origin and touching the circle C externally. Then the radius of T is equal to