Bunuel wrote:
Two circles overlap such that the center of each circle lies on the circumference of the other. What is the circumference of one circle?
(1) The longest distance between any two points on the circles is 9.
(2) The area of one circle is 9π.
Kudos for a correct solution.
When two circles overlap such that their centers are on each other's circumference, their radii will be equal. The diagram will help you understand this.
Attachment:
Ques3.jpg
Besides, the format of the question should give you a hint that the circumference of the two circles should be the same.
"What is the circumference of one circle?"
If the two circles had difference radii, they would have specified the circle for which they wanted the circumference or they would have asked for the circumferences of the two circles.
Circle1 has center at C1 and its radius will be the distance of C1 from its circumference. One point on the circumference is C2 so its radius will be equal to distance between C1 and C2. Similarly, the radius of circle 2 will be distance between C2 and C1. Hence both will have the same radii.
To get circumference, all you need is the value of any one defined aspect of the circles.
Statement 1 gives you the diameter which gives you the circumference.
Statement 2 gives you the area of the circles which gives you the radius and hence the circumference.
Answer (D)
I marked Stmnt 1 - Insufficient initially but later figured out my mistake