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

 

 

 

hey keerthana, you've made an error by saying "OD ² +OB ² =OD ²"

the answer is 19 cm

construction:  OM || BD

STEPS:

By BPT when OM||BD,
AO/BO = AM/DM 
But, AO = BO
=> AM/DM = 1 or AM = DM

Also, L MOD = L BDO = 90⁰ (alternate angles)

Now, BD² = OB² - OD² = 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 = √OM² + OD² = √105/4 + 64 = √105 + 256 / 2 = √361 / 2
or, DM = √361 / 2
Hence, AD = 2 DM = √361 = 9

                                                                                                                                           - credits @smartrahul

and hope that helps jahnavi. By the way, where did u get that question from?