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# C1 Circles Exclusion Watch

1. Question: Prove that each of the circles x2+y2-4x=0 and x2+y2-12x-8y+43=0 lie completely outside each other.

Attempt: I worked out the centres as (2,0) and (6,4) respectively, and the radii as 2 and 3 respectively. But now how do I finish answering the question.
Question: Prove that each of the circles x2+y2-4x=0 and x2+y2-12x-8y+43=0 lie completely outside each other.

Attempt: I worked out the centres as (2,0) and (6,4) respectively, and the radii as 2 and 3 respectively. But now how do I finish answering the question.
Find the shortest distance between the two centres of the circle.
Show that the radii are shorter than this.
3. how do you find the shortest distance between the circles' centres???
4. (Original post by Maphs)
how do you find the shortest distance between the circles' centres???
The straight line between the two points?
5. (Original post by joostan)
Find the shortest distance between the two centres of the circle.
Show that the radii are shorter than this.
Would that be both radii combined? (i.e. 2+3)

It's a little awkward to recognize that 4*root 2 is larger than 5 without a calculator under exam pressure
Would that be both radii combined? (i.e. 2+3)

It's a little awkward to recognize that 4*root 2 is larger than 5 without a calculator under exam pressure

Its just surds.
4root(2) = root(32)
5 = root(25)
32>25
7. how did you get 4 root 5?
8. (Original post by Maphs)
how did you get 4 root 5?
You mean 4root2? I would have left it as root(32) to be honest - the distance between the centres.
9. (Original post by davros)
You mean 4root2? I would have left it as root(32) to be honest - the distance between the centres.
Yes then it's more obvious that root(32) is greater than root(25) so the circles do not touch.

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Updated: March 28, 2013
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