Circle A has a center at $(2, 3)$ $(2 ,3 )$ and a radius of $5$ $5$ . Circle B has a center at $(3, 8)$ $(3 ,8 )$ and a radius of $1$ $1$ . Do the circles overlap? If not what is the smallest distance between them?

Question

Circle A has a center at $(2, 3)$ $(2 ,3 )$ and a radius of $5$ $5$ . Circle B has a center at $(3, 8)$ $(3 ,8 )$ and a radius of $1$ $1$ . Do the circles overlap? If not what is the smallest distance between them?

1 Answer

Impact of this question

2193 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-02-04T01:15:40

If the two circles touched at a single point , then the distance between the centers would be $5 + 1 = 6$ $5+1=6$ and the distance between the circles would be zero.

Explanation:

Using the distance formula, the actual distance between the two centers is:

$\sqrt{{(8 - 3)}^{2} + {(3 - 2)}^{2}} = \sqrt{26} \approx 5.1$ $sqrt[(8-3)^2+(3-2)^2]=sqrt26~~5.1$

Since the distance $5.1 < 6$ $5.1<6$ , the two circles must overlap !

Hope that helped

enter image source here

Science

Math

Humanities

... and beyond

Circle A has a center at $(2, 3)$ $(2 ,3 )$ and a radius of $5$ $5$ . Circle B has a center at $(3, 8)$ $(3 ,8 )$ and a radius of $1$ $1$ . Do the circles overlap? If not what is the smallest distance between them?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

Circle A has a center at (2,3)(2 ,3 ) and a radius of 55 . Circle B has a center at (3,8)(3 ,8 ) and a radius of 11 . Do the circles overlap? If not what is the smallest distance between them?

1 Answer

Explanation:

Related questions

Impact of this question

Circle A has a center at $(2, 3)$ $(2 ,3 )$ and a radius of $5$ $5$ . Circle B has a center at $(3, 8)$ $(3 ,8 )$ and a radius of $1$ $1$ . Do the circles overlap? If not what is the smallest distance between them?