## Circle How do you prove that two circles...

### SomethingTypical

Posted 07 December 2004 - 08:01 PM

How do you prove that two circles just touch each other?

Thanks

Thanks

### Infinite_Dreams

Posted 08 December 2004 - 09:51 PM

I did it by:

If the sum of the two radii = the distance from one center to another, then they touch at one point.

If the sum of the two radii > the distance from one center to another, then they touch at two points.

If the sum of the two radii < the distance from one center to another, then they don't touch.

If the sum of the two radii = the distance from one center to another, then they touch at one point.

If the sum of the two radii > the distance from one center to another, then they touch at two points.

If the sum of the two radii < the distance from one center to another, then they don't touch.

### Discogirl17

Posted 08 December 2004 - 10:10 PM

That is infact how you do it, remember if the distance isnt just a horizontal or vertical line you can form a sort of right-angeld triangle between the two centres with distance (d) as the hypotenuse and use pythagoras to calculate it.

### Infinite_Dreams

Posted 09 December 2004 - 05:41 PM

I'd use the distance formula. Eg. if one circle (arbitrarily) had equation (x-4)^2 + (y+1)^2 = 25 and the other (also arbitrarily) (x+1)^2 + (y-1)^2 = 16 then I'd find the center of both circles using (-g, -f) -> (-1, 1) and (4, -1). Use distance formula, the compare this with the sum of the radii (will be 9 here).

### fresh graduate

Posted 10 December 2004 - 02:15 PM

[B][I][FONT=Times][SIZE=7][COLOR=purple]Actually I think itâ€™s the right answer to this question

### Joel

Posted 28 January 2006 - 03:59 PM

QUOTE(Amo @ Jan 27 2006, 10:36 AM)

Hi, just a quick question... when you are asked to write down the equation of a circle in the exam, can you leave it in the form (x-a)^2+(y-b)^2=r^2, or do you have to expland the brackets?

Thanks

Thanks

You only need to expand the brackets if the question asks you to give the equation of the circle in expanded form.