Common tangent to two circles

In figure, AB and CD are common tangents to two circles of equal radii. Prove that AB=CD.

In the figure, PQ and RS are the common tangents to two circles intersecting at O. Prove that PQ=RS

In figure, AB and CD are common tangents to two circles of unequal radii. Prove that AB=CD

The point of intersection of direct common tangents and transverse common tangents to two circles divide the line segmenta joining the two centres externally and internally respectively in the ratio of their radii.

AB and CD are common tangents to two circles which intersect each other at C as shown in the figure IF AB = 6cm , find CD.

Two circle with radii r_(1) and r_(2) respectively touch each other externally. Let r_(3) be the radius of a circle that touches these two circle as well as a common tangents to two circles then which of the following relation is true

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_(1)P,C_(1)C_(2) are C_(1) Q are in

(ii) The radical axis bisects the common tangents of two circles.

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

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