Question

Circle A has a radius of `5` and a center of `(3 ,2 )`. Circle B has a radius of `3` and a center of `(1 ,4 )`. If circle B is translated by `<2 ,-1 >`, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Answer 1

circle B inside circle A

Explanation:

What we have to do here is `color(blue)"compare"` the distance ( d) between the centres of the circles to the `color(blue)"sum/difference of the radii"`

• If sum of radii > d , then circles overlap

• If sum of radii < d , then no overlap

• If difference of radii > d , then one circle inside the other

Before calculating d we must find the ' new' centre of B under the given translation which does not change the shape of the circle only it's position.

Under a translation `((2),(-1))`

`(1,4)to(1+2,4-1)to(3,3)larr" new centre of B"`

Since the centres (3 ,2) and (3 ,3) have the same x-coordinate they lie on the vertical line with equation x = 3 and d is the difference of the y-coordinates.

`rArrd=3-2=1`

difference of radii= radius of A - radius of B = 5 - 3 = 2

Since difference of radii > d , then circle B is inside circle A.
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