+2115 Two circles intersect at two points, $P$ and $Q$. The equations of the two circles are $x^2 + (y - 1)^2 = 1$ and $(x - 1)^2 + y^2 = 1$. Find the length PQ.
+129771 Since both of the radiuses = 1, set these circles =
x^2 + (y-1)^2 = (x -1)^2 + y^2
x^2 + y^2 - 2y + 1 = x^2 -2x + 1 + y^2
-2y =-2x
x = y
So
x^2 + (x -1)^2 = 1
x^2 + x^2 -2x + 1 =1
2x^2 - 2x = 0
x^2 -x =0
x ( x -1) = 0
x=0 x=1
The intersection points are (0,0) and (1,1)
PQ = sqrt [1 + 1] = sqrt 2
