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