CAT 2004 — QA Question 17

2 CirclesEasy

Passage / Data

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 ratio of the length of PQ to that of QO?

Answer & solution

A
1 : 4
1 : 3
C
3 : 8
D
3 : 4

Solution

ΔSQO ~ ΔRPO

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

⇒ $\frac{1.5}{2}$ = $\frac{28 - 3.5 x}{28}$

⇒ 42 = 56 – 7x

⇒ x = 2

⇒ PQ = 7 cm, OQ = 21 cm

∴ PQ : OQ = 1 : 3

Hence, option (b).

CAT 2004 QA Q17: What is the ratio of the length of PQ to that of QO? — Solution | TheCATExam