Two circles of same radii r and centres O and O' touch each other at P as shown in Fig. 10.91. 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' =
Given:
AO’ = r
O’P = r
PO = r
AO = AO’ + O’P + PO
⇒ AO = r + r + r
⇒ AO = 3r
Now,
Hence, AO: AO’ = 3