CAT 1993 — QA Question 17
2 CirclesEasy
The line AB is 6 metres in length and is tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is
Answer & solution
5 metres
- B
4 metres
- C
6 metres
- D
3 metres
Solution
Let x meters and y meters be the radius of the outer and the inner circles respectively and O be their center.
In right angled Δ OCB,
CB2 = OB2 - OC2
⇒ 9 = x2 – y2
⇒ (x + y) ( x – y) = 9 × 1
As x and y are integers, therefore, x + y = 9 and x – y = 1.
Thus, x = 5.
Hence, radius of the outer circle is 5 meters.
Hence, option (a).