`r_(1),r_(2)` are the radii of two non-intersecting circles having `A,B` as centres.If `P` is the centre of `AB` then the perpendicular distance of `P` form their radical axis is

From an external point P, two tangents PAandPB are drawn to the circle with centre O .Prove that OP is the perpendicular bisector of AB.

R and r are the radii of two circles (R > r). If the distance between the centres of the two circles be d, then length of common tangent of two circles is

(a,c) and (b,c) are the centres of two circles whose radical axis is the y-axis.If the radius of the first circle is r then the diameter of the other circle is

If from any point P, tangents PT, PT' are drawn to two given circles with centres A and B respectively, and if PN is the perpendicular from P on their radical axis, then PT^(2) – PT'^(2) =

R and r are the radius of two circles (R gt r) . If the distance between the centre of the two circles be d , then length of common tangent of two circles is

The given figure shows a circle with centre O. P is mid-point of chord AB. Show that OP is perpendicular to AB.

Let r _(1) and r _(2) be the radii of the largest and smallest circles, respectively, which pass through the point (–4,1) and having their centres on the circumference of the circle x ^(2) + y ^(2) + 2x + 4y - 4 =0 . If (r _(1))/(r _(2)) = a + b sqrt2. then a + b is equal to .

From any point P tangents of length t_(1) and t_(2) are drawn to two circles with centre A,B and if PN is the perpendicular from P to the radical axis and t_(1)^(2) - t_(2)^(2) = K.PN*AB then K=