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' =

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

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