# CAT 2004 | Question: 58

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Answer the question on the basis of the information given below:

In the adjoining figure, I and II are circles with centres 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 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.

The length of SO is

1. $8 \sqrt{3}$ cm
2. $10 \sqrt{3}$ cm
3. $12 \sqrt{3}$ cm
4. $14 \sqrt{3}$ cm

PR/QS =2/1.5

We know,

PR/QS=PO/QO (PRO and QSO are similar triangles)

or, QO=28⨉1.5/2=21

Now for a right angle triangle $QS^2 +SO^2=QO^2$

Here,SO=$\sqrt{21^2-(1.5)^2}=20.94$

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