Answer the questions on the basis of the information given below :In the adjoining figure, I and II are circles with centers P and Q respectively. The two circles touch each other and have a common tangent that touches them at points R and S respectively. This common tangent meets the line joining P and Q at O. The diameters of I and II are in the ratio 4 : 3. It is also known that the length of PO is 28 cm.

What is the ratio of the length of PQ to that of QO? (2004)

1:4

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1:3

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3:8

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3:4

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Solution

The correct option is B 1:3
From the given diagram,

$\frac{O Q}{S Q} = \frac{O P}{R P}$

$\frac{O Q}{O P} = \frac{S Q}{R P} = \frac{3}{4}$

Therefore, $\frac{P Q}{O Q} = \frac{1}{3}$

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is--

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The correct option is B 1:3From the given diagram, OQSQ=OPRP OQOP=SQRP=34 Therefore, PQOQ=13

The correct option is B 1:3
From the given diagram,

$\frac{O Q}{S Q} = \frac{O P}{R P}$

$\frac{O Q}{O P} = \frac{S Q}{R P} = \frac{3}{4}$

Therefore, $\frac{P Q}{O Q} = \frac{1}{3}$