The internal common tangents to two circles with centre `C_1` and `C_2` intersect the line joining `C_1` and` C_2` at P and the two direct common tangents intersects the line joining `C_1` and `C_2` at Q. The length `C_1P`, `C_1C_2` and `C_1` Q are in

The internal common tangents to two circles with centre C_1 and C_2 intersect the line joining C_1 and C_2 at P and the two direct common tangents intersects the line joining C_1 and C_2 at Q. The length C_1P , C_1C_2 are C_1 Q are in

Suppose that two circles C_(1) and C_(2) in a plane have no points in common. Then

Transverse common tangents are drawn from O to the two circles C_1,C_2 with 4, 2 respectively. Then the ratio of the areas of triangles formed by the tangents drawn from O to the circles C_1 and C_2 and chord of contacts of O w.r.t the circles C_1 and C_2 respectively is

In Figure, two circles touch each other at the point C . Prove that the common tangent to the circles at C , bisects the common tangent at P and Q .

In the figure, two circles touch each other at the point C.Prove that the common tangents to the circles at C, bisect the common tangents at P and Q.

The tangent to the curve y=e^x drawn at the point (c,e^c) intersects the line joining (c-1,e^(c-1)) and (c+1,e^(c+1)) (a) on the left of n=c (b) on the right of n=c (c) at no points (d) at all points

Find value of c such that line joining the points (0, 3) and (5, -2) becomes tangent to curve y=c/(x+1)

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

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

Let C_1 and C_2 are circles defined by x^2+y^2 -20x+64=0 and x^2+y^2+30x +144=0 . The length of the shortest line segment PQ that is tangent to C_1 at P and to C_2 at Q is