Review question

# Can we show that these two circles touch? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6100

## Suggestion

Show that the circles having equations $x^2 + y^2 = 25$ and $x^2 + y^2 - 24x - 18y + 125 = 0$ touch each other. Calculate the coordinates of the point at which they touch.

Could I sketch the two circles and observe what is happening?

If the two circles touch, then in how many points do they intersect?

Could we solve the two equations simultaneously?

How could I do this as neatly as possible, and how many solutions would I expect?