sapuna wrote:Three circles with radii 1, 2 , 3, respectively, lie on the same plane. Do any of these circles intersect or lie completely within each other ?
1) IF you connect the centers of the circles, an equaliteral triangle is formed with a height of 2 square root of 3.
2) The distance between any two centers is less than 6.
Figure 1:
![Image](https://s18.postimg.cc/6lnb1q3xh/circles_A_B_and_C.jpg)
In the figure above, x, y and z represent the distances between circles A, B and C.
∆ABC is formed by joining the 3 centers.
Statement 1: If you connect the centers of the circles, an equaliteral triangle is formed with a height of 2 square root of 3.
Figure 2:
![Image](https://s28.postimg.cc/x97b83zmx/equiilateral_triangle_ABC.jpg)
Thus, each side of ∆ABC = 4.
In figure 1, BC=4 only if z<0, implying that circles B and C intersect.
SUFFICIENT.
Statement 2: The distance between any two centers is less than 6.
It's possible that x=y=z=0, in which all 3 circles intersect.
It's possible that x=y=z=1/2, in which case none of the circles intersect.
INSUFFICIENT.
The correct answer is
A.
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