+948 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.
+129852 The circles have the same radius....set their equations equal
x^2 + (y -1)^2 = (x-1)^2 + y^2
x^2 + y^2 - 2y + 1 = x^2 -2x + 1 + y^2
-2y =-2x
y = x
So
x^2 + ( x -1)^2 =1
2x^2 - 2x + 1 = 1
2x^2 - 2x =0
x^2 - x =0
x ( x -1) = 0
Solving this produces x =0 and x =1
Since x = y
x = 0 y = 0
x =1 y =1
Points of intersection are (0,0) and (1,1)
PQ = sqrt [ (1-0)^2 + (1-0)^2 ] = sqrt 2
