Q10 of 47 Page 1

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

We have to prove AB = CD.

Let P be the point of intersection of AB and CD.


We know that the length of two tangents drawn from an external point to a circle is equal.


∴ AP = CP … (1)


BP = DP … (2)


Adding (1) and (2), we get


⇒ AP + BP = CP + DP


⇒ AB = CD


Ans. Hence proved that AB = CD.


More from this chapter

All 47 →
30

Two points A and B are on the same side of a tower and in the same straight line with its base. The angles of depression of these points from the top of the tower are 60° and 45° respectively. If the height of the tower is 15 m, then find the distance between these points.

 31

The height of a cone is 30 cm. From its topside a small cone is cut by a plane parallel to its base. If volume of smaller cone is 1/27 of the given cone, then at what height it is cut from its base?

 18

If the pth term of an A. P. is q and qth term is p, prove that its nth term is (p + q – n).

 19

A solid metallic sphere of diameter 16 cm is melted and recasted into smaller solid cones, each of radius 4 cm and height 8 cm. Find the number of cones so formed.