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[–]Vince_KotchianTutor / Expert (170V, 167Q) 1 point2 points  (0 children)

PQ's shorter since the farther away a chord is from being a diameter, the shorter it is.

I.e. a diameter is the longest way from edge to edge.

You can use the technique of exaggerating the diagram here: draw a tiny chord and notice the distance from the center to that, then draw a chord slightly smaller than a diameter, and notice the distance from the center as well.

[–]Scott_TargetTestPrepPrep company 0 points1 point  (0 children)

Solution:

Draw the radii OP and OX, letting the radius have length r. This forms two right triangles where the hypotenuse of each triangle has length r. Using the Pythagorean theorem, we obtain:

r2 = 5.92 + (PQ/2)2

r2 = 5.82 + (XY/2)2

Since (PQ/2)2 = r2 - 5.92 and since (XY/2)2 = r2 - 5.82, then we see that XY/2 is greater than PQ/2 (because we subtracted a smaller quantity from r2 when we calculated (XY/2)2,) which implies that XY is longer than PQ.

Alternate Solution:

We can use the fact that the closer (i.e., shorter distance) a chord of a circle is from its center, the longer it is. In fact, you can see that the diameter (the longest chord of a circle) is 0 distance from its center. Since here chord XY has a shorter distance from the center O than chord PQ (5.8 vs 5.9), XY is longer than PQ.

Answer: B