CAT 2003 Slot 1 — QA Question 23
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
Each question is followed by two statements, A and B. Answer each question using the following instructions
Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.
AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle?
A. AB is not a diameter of the circle
B. The distance between AB and the tangent at E is 5 cm
Answer & solution
1
- B
2
- C
3
- D
4
Let radius of circle be r.
AC = 2.5 as radius bisects the chord.
Using statement A alone:
We have been told that AB is not a diameter of the circle. But it does not give us any useful information to solve the problem.
So, statement A alone is not sufficient to answer the question.
Using statement B alone:
From the figure above, CE = 5
∴ OC = r − 5
∴ OA2 = OC2 + AC2
∴ r2 = (r − 5)2 + (2.5)2
Solving the above equation,
r = 3.125 cm
So, statement B alone is sufficient to answer the question.
Hence, option (a).