Maths-
General
Easy
Question
If d is the distance between the centres of two circles, 
are their radii and 
, then
- The circles touch each other externally
- The circles touch each other internally
- The circles cut each other
- The circles are disjoint
Hint:
We are given the radii of two circles and distance between them. We have to find the position of the cricles with respect to each other. We will use the distance between them to solve the question.
The correct answer is: The circles touch each other externally
The radii of the circles are r1 and r2.
The distance between the cricles is d = r1 + r2
We will check all the options one by one.
1) Circles touch each other externally.
If the circles are touching externally, they will be touching each other only at a single point.
The distance of the that point from its center will be the radius.
So, the distance between the centers of the cricle will be the sum of the radii.
d = r1 + r2
The given option is correct.
2)Circles are disjoint.
It means there is distance between the circles.
So, the distance between the centers will be the sum of the radii and some extra distance.
This option is wrong.
3) The circles cut each other.
It means the distance between the center of one circle and the the outer boundary of the circle will be less than it's radius of one circle. For another circle it will be just radius.
The distance is less than sum of the radii.
This option is wrong.
4) The circle touches internally.
If the circles are touching internally their radii will overlap.
The distance between the two centers will be less than the radius of the outer circle.
So, the distance is less than the sum of the radii.
This option is wrong.
For such questions, we have to see how the cricles are with respect to each other to find the distance between the centers.
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