Prove that a common tangent to two circles is bisected by the radical axis.

In Fig.10.21, 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.( FIGURE )

Common Tangents of Circles

Prove that a diameter of a circle which bisects a chord of the circle also bisects the angle subtended by the chord at the centre of the circle.

The length of a common internal tangent to two circles is 5 and that of a common external tangent is 13. If the product of the radii of two circles is lamda , then the value of (lamda)/(4) is

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

If the length of a common internal tangent to two circles is 7, and that of a common external tangent is 11, then the product of the radii of the two circles is (A) 36 (B) 9 (C) 18 (D) 4

The length of common internal tangent to two circles is 7 and that of a common external tangent is 11. Then the product of the radii of the two circles is

The length of a common internal tangent to two circles is 5 and a common external tangent is 15, then the product of the radii of the two circles is :

Two circle touch each other externally at the point (0,k) and y-axis is the common tangent to these circles. Centres of these circle lie on the line

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