Thread: Intersecting Circles

Hi there,

I'm doing this question:

A circle has the centre (-4,-2) and radius √58. A second circle has equation (x-4)² + (y-6)² = 26. Find the distance between the centres of these two circles and hence show that the circles intersect.

I know how to find the distance, however I don't know how to show that circles intersect.

Thank you in advance ^_^

Originally Posted by HighlyFlammable

Hi there,

I'm doing this question:

A circle has the centre (-4,-2) and radius √58. A second circle has equation (x-4)² + (y-6)² = 26. Find the distance between the centres of these two circles and hence show that the circles intersect.

I know how to find the distance, however I don't know how to show that circles intersect.

Thank you in advance ^_^

If the circles touch, ie intersect at one point, then you can easily show that the distance between the two centers must be equal to the sum of the radii of the two circles. In your case the distance between the two centers is less than the sum of the two radii. That means the centers are closer than in the case when they are touching. What does that mean about the number of intersection points?

-Dan