Two circles overlap such that the center of each circle lies on the circumference of the other. What is the

[BTGmoderatorDC]

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.




OA D

Source: Veritas Prep

[swerve]

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.




OA D

Source: Veritas Prep

Statement 1: Since the longest distance between any two points on the circles is 9 and Two circles overlap such that the center of each circle lies on the circumference of the other.

Assuming radius of circle is r , \(3R = 9\, \Rightarrow \, R = 3.\, \Large{\color{green}\checkmark}\)

Statement 2: The area of one circle is \(9\pi.\)

\(\pi \cdot R^2 = 9 \cdot \pi\)
\(\Rightarrow\, R = 3.\, \Large{\color{green}\checkmark}\)

Hence both statements are sufficient, the correct answer is D.