CAT 2004 — QA Question 18
Answer the following question based on 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 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 radius of the circle II?
Answer & solution
- A
2 cm
3 cm
- C
4 cm
- D
5 cm
Radius of circle II = 1.5 × 2 = 3 cm.
Hence, option (b).
Alternately,
We can solve this question and the previous question together using options as follows:
Consider each of the options in this question.
Option (a): If the radius of circle II is 2, the radius of I is 8/3. PQ is then 14/3 and OQ is 70/3.
∴ PQ : OQ = 1 : 5, which is not there in the options of the previous question.
Option (b): If the radius of circle II is 3, the radius of I is 4. PQ is then 7 and OQ is 21.
∴ PQ : OQ = 1 : 3, which is there in the options of the previous question. This is possible.
Option (c): If the radius of circle II is 4, the radius of I is 16/3. PQ is then 28/3 and OQ is 56/3.
∴ PQ : OQ = 1 : 2, which is not there in the options of the previous question.
Option (d): If the radius of circle II is 5, the radius of I is 20/3. PQ is then 35/3 and OQ is 49/3.
∴ PQ : OQ = 5 : 7, which is not there in the options of the previous question.
∴ The radius of circle II is 3 and PQ : OQ = 1 : 3
Hence, option (b).