Note that both triangles OPQ and OXY are both isosceles triangles (OP=OQ=OX=OY=radius of the circle) => the height drawn from O to either bases cut the chord PQ and XY in equal halt => by Pythagorean theorem: radius^2 = (5.9)^2+(PQ/2)^2 = (5.8)^2+(XY/2)^2. Since (5.9)^2>(5.8)^2 => (PQ/2)^2<(XY/2)^2 => PQ<XY (PQ and XY are positive of course) => B is answer.

You could go on full length to prove this but there's just one thing to remember here: The closer to the center, the longer the chord (here we talk about the distance between the center and the point on the chord that's closest to the center)

When it's the furthest from the center it's 0 and when it's closest the length becomes the diameter.

XY is closer to the center so XY is longer.
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Yuan Liu, Creator of Gregory. Dartmouth Grad.

For More GRE Math Resources

how do we infer that the perpendicular from center of circle to PQ or XY cuts it into half?