Question

Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. If 00' is produced to meet the circle C (O', r) at A and AT is a tangent to the circle C(O, r) such that O'Q ⊥ AT. Then AO: AO' =

A. 3/2 

B. 2 

C. 3

 D. 1/4

Answer 1

Answer is C. 3

Given: 

AO’ = r 

O’P = r 

PO = r 

AO = AO’ + O’P + PO 

⇒ AO = r + r + r 

⇒ AO = 3r 

Now,

\(\frac{AO}{AO'}=\frac{3r}{r}\) = 3

Hence, AO: AO’ = 3