Two circles of same radii r and centres O and O' touch each other at P

1.	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» 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

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»

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

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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

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