+1206 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.
+129656 Since
(1) = (1) set the equations =
x^2 + (y-1)^2 = (x-1)^2 + y^2 simplify
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
y = 0 y = 1
The intersection points are ( 0, 0) and (1, 1)
The distance between them = sqrt [1^2 + 1^2] = sqrt 2
