The radii of two concentric circles are 13 cm and 8 cm . AB is a diameter of the bigger circle BD is tangent to the smaller circle touching it at D.Find the length of AD

We draw a line parralel to BD from O on AD at M such that OM || BD

By thales' theorem or basic proportionality theroem , or similarity

AO/BO = AM/DM

But, AO = BO

=> AM/DM = 1 or AM = DM

Also, ** L**MOD =

*ODM = 900 (alternate angles)*

**L**Now, BD

^{2}= OB

^{2}- OD

^{2}= 169 - 64 =105

or, BD = √105 cm

Again, since OM || BD

so, by similarity

OM/BD = AO/AB

=> OM = BD X AO / AB = √105 x 13 / 26 = √105 / 2

or, OM = √105 / 2

So in triangle ODM

DM = √OM

^{2}+ OD

^{2}= √105/4 + 64 = √105 + 256 / 2 = √361 / 2

or, DM = √361 / 2

Hence, AD = 2 DM = √361

hope this helps you frnd........