+501 The circle centered at $(2,-1)$ and with radius $4$ intersects the circle centered at $(2,5)$ and with radius $\sqrt{10}$ at two points $A$ and $B$. Find $(AB)^2$.
Equation of circle centered at (h,k) with radius r:
\[(x - h)^2 + (y - k)^2 = r^2.\]
$(AB)^2 = 18$
+1639 The circle centered at (2, -1) and with radius 4 intersects the circle centered at (2, 5) and with radius √10 at two points A and B. Find (AB)2.
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Let the centers of the circles be P(2, -1) and Q(2, 5) PQ = |-1 + 5| = 6
Let the midpoint of AB be M. AM = BM ==> x
sqrt(AP2 - x2) + sqrt(AQ2 - x2) = PQ x = (√15) / 2
AB2 = (2x)2
AB2 = 15
