Question

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

Answer 1

it will be 19cm,
 
If you can draw the figure correctly I am only writing the solution,
 
Join the center of circles to D and also join A to E by a line segment.
triangle BCD and ABE are right angled triangles right angled at D and E respectively.
Now,
BD^2=(13-8)*(13+8)
=>BD=sqrt(105)
 
say, angle ABD=angle ABE =theta,
tan(theta)=CD/BD =8/r00t(105),
cos(theta)=root(105)/13,
 
also, cos(theta)=BE/AB=BE/26
=>root(105)/13=BE/26
=>BE=2*root(105)
=>DE=root(105)
 
AE/BE=tan(theta)=8/root(105)=> AE=16
 
In Triangle ADE, use Pythagoras theorem
AE^2+DE^2=AD^2
=>AD=root(16^2+105)
=>AD=root(361)
=>AD=19cm