The circles $x^2 + y^2 = 4$ and $(x - 5)^2 + (y - 8)^2 = 60$ intersect in two points $A$ and $B.$ Find the distance $AB$.

sandwich Aug 24, 2023

#1**0 **

The first circle has center (0,0) and radius 2, and the second circle has center (5,8) and radius 10. The two circles intersect when the distance between their centers is equal to the sum of their radii, or when [\sqrt{(0 - 5)^2 + (0 - 8)^2} = 2 + 10.]Solving, we find that the two circles intersect at (5,8) and (−5,8). The distance between these points is 10.

Guest Aug 24, 2023