If the equations of two circles, whose radii are r and R respectively, be S = 0 and S' = 0, then prove that the circles`S/r+-(S')/R=0`will intersect orthogonally

The condition for two circles with radii and r_(1) and r_(2) be the distance between their centre,such that the circles are orthogonal is

1If r and R be the radii of inner and outer circles respectively,then area of ring is

If the sum of the areas of two circles with radii R_1 and R_2 is equal to the area of a circle of radius R, then

The equation of any circle passing through the points of intersection of the circle S=0 and the line L=0 is

Find the equation of the circle when the end points of a diameter of the circle are : (p, q) and (r, s)

If two circles S=0 and s'=0 are touch each other externally then

If the sum of the circumferences of two circles with radii R_1 and R_2 is equal to the circumference of a circle of radius R, then

If P and Q a be a pair of conjugate points with respect to a circle S . Prove that the circle on PQ as diameter cuts the circle S orthogonally.

Let S=0 and S'=0 be two intersecting circles with radii 2 and 3. Their point of intersection areA and B. Let AC and AD be diameter of S=0 and S'=0 respectively.If angle between the circles is theta where cos theta=1/4 then CD equals.

The circles having radii r1 and r2 intersect orthogonally Length of their common chord is